12th Mathematics - Book Back Answers - Chapter 5 - English Medium Guides

  

 

Plus Two / 12th Mathematics - Book Back Answers - Chapter 5 - English Medium

Tamil Nadu Board 12th Standard Mathematics - Chapter 5: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 5 from the Tamil Nadu State Board 12th Standard Mathematics textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 5 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

 

I. Multiple Choice Questions

1. The equation of the circle passing through (1,5) and (4,1) and touching y -axis is
x² + y² − 5x − 6y + 9 +λ (4x + 3y −19) = 0where λ is equal to
(1) 0, -$\frac{\mathbf{40}}{\mathbf{9}}$
(2) 0 

(3) $\frac{\mathbf{40}}{\mathbf{9}}$
(4) $\frac{\mathbf{-}\mathbf{40}}{\mathbf{9}}$
Answer Key:
(1) 0, -$\frac{\mathbf{40}}{\mathbf{9}}$

$\frac{\mathbf{ }}{}$
2. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half
the distance between the foci is
(1) $\frac{\mathbf{4}}{\mathbf{3}}$
(2) $\frac{\mathbf{4}}{\sqrt{\mathbf{3}}}$ 
(3) $\frac{\mathbf{2}}{\sqrt{\mathbf{3}}}$
(4) $\frac{\mathbf{3}}{\mathbf{2}}$
Answer Key:
(3) $\frac{\mathbf{2}}{\sqrt{\mathbf{3}}}$

3. The circle x2 + y2 = 4x + 8y + 5intersects the line3x − 4y = m at two distinct points if
(1) 15 < m < 65 

(2) 35 < m < 85 

(3) −85 < m < −35 

(4) −35 < m <15
Answer Key:
(4) −35 < m <15

 
4. The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes
through the point (2,3) .
(1) $\frac{\mathbf{6}}{\mathbf{5}}$

(2) $\frac{\mathbf{5}}{\mathbf{3}}$

(3) $\frac{\mathbf{10}}{\mathbf{3}}$

(4) $\frac{\mathbf{3}}{\mathbf{5}}$

Answer Key:
(3) $\frac{\mathbf{10}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
5. The radius of the circle 3x² + by² + 4bx − 6by + b² = 0 is
(1) 1 

(2) 3 

(3) $\sqrt{\mathbf{10}}$

(4) $\sqrt{\mathbf{11}}$
Answer Key:
(3) $\sqrt{\mathbf{10}}$

6. The centre of the circle inscribed in a square formed by the lines x² −8x −12 = 0 and  y² −14y + 45 = 0 is
(1) (4,7) 

(2) (7, 4) 

(3) (9,4) 

(4) (4,9)
Answer Key:
(1) (4,7) 

 
7. The equation of the normal to the circle x² + y² − 2x − 2y +1 = 0  which is parallel to the line
2x + 4y = 3 is
(1) x + 2y = 3 

(2) x + 2y + 3 = 0 

(3) 2x + 4y + 3 = 0 

(4) x − 2y + 3 = 0
Answer Key:
(1) x + 2y = 3 

 
8. If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3,0) and F₂ (-3,0) then PF₁ + PF₂  
is
(1) 8 

(2) 6 

(3) 10 

(4) 12
Answer Key:
(3) 10 

 
9. The radius of the circle passing through the point (6, 2) two of whose diameter are x + y = 6
and x + 2y = 4 is
(1) 10 

(2) $\mathbf{2}\sqrt{\mathbf{5}}$

(3) 6 

(4) 4
Answer Key:
(2) $\mathbf{2}\sqrt{\mathbf{5}}$

10. The area of quadrilateral formed with foci of the hyperbolas $\frac{{\mathit{x}}^{\mathbf{2}}}{{\mathit{a}}^{\mathbf{2}}}\mathbf{-}\frac{{\mathit{y}}^{\mathbf{2}}}{{\mathit{b}}^{\mathbf{2=1\; and }}}$$\frac{{\mathit{x}}^{\mathbf{2}}}{{\mathit{a}}^{\mathbf{2}}}\mathbf{-}\frac{{\mathit{y}}^{\mathbf{2}}}{{\mathit{b}}^{\mathbf{2=-1}}}$$\frac{{\mathbf{}}^{}}{}$
is
(1) 4(a² + b²)

(2) 2(a² + b²) 

(3) a² + b²

(4) $\frac{\mathbf{1}}{\mathbf{2}}$(a² + b²)$\frac{\mathbf{}}{}$
Answer Key:

(2) 2(a² + b²) 

11. If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents
to the circle (x − 3)² + ( y + 2)² = r² , then the value of r² is
(1) 2 

(2) 3 

(3) 1 

(4) 4
Answer Key:
(1) 2 

 
12. If x + y = k is a normal to the parabola y²=12x , then the value of k is
(1) 3 

(2) -1 

(3) 1 

(4) 9
Answer Key:
(4) 9

 
13. The ellipse ${\mathit{E}}_{\mathbf{1}}$: $\frac{{\mathit{x}}^{\mathbf{2}}}{\mathbf{9}}\mathbf{-}\frac{{\mathit{y}}^{\mathbf{2}}}{\mathbf{4}}$=1is inscribed in a rectangle R whose sides are parallel to the
coordinate axes. Another ellipse  passing through the point (0, 4) circumscribes the rectangle
R . The eccentricity of the ellipse is
(1) $\frac{\sqrt{\mathbf{2}}}{\mathbf{2}}$

(2) $\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}$

(3) $\frac{\mathbf{1}}{\mathbf{2}}$

(4) $\frac{\mathbf{3}}{\mathbf{4}}$

Answer Key:
(3) $\frac{\mathbf{1}}{\mathbf{2}}$

$\frac{\mathbf{ }}{}$
14. Tangents are drawn to the hyperbola $\frac{{\mathbf{x}}^{\mathbf{2}}}{\mathbf{9}}\mathbf{-}\frac{{\mathbf{y}}^{\mathbf{2}}}{\mathbf{4}}$=1parallel to the straight line 2x − y =1. One of
the points of contact of tangents on the hyperbola is
(1)

(2)
(3)
(4)

Answer Key:
(3)

$$
15. The equation of the circle passing through the foci of the ellipse $\frac{{\mathbf{x}}^{\mathbf{2}}}{\mathbf{16}}\mathbf{+}\frac{{\mathbf{y}}^{\mathbf{2}}}{\mathbf{9}}$ =1having centre at
(0,3) is
(1) x² + y² − 6y − 7 = 0

(2) x² + y² − 6y + 7 = 0
(3) x² + y² − 6y − 5 = 0 

(4) x² + y² − 6y + 5 = 0
Answer Key:
(1) x² + y² − 6y − 7 = 0 

 
16. Let C be the circle with centre at (1,1) and radius =1. If T is the circle centered at (0, y)
passing through the origin and touching the circleC externally, then the radius of T is equal
to
(1) $\frac{\sqrt{\mathbf{3}}}{\sqrt{\mathbf{2}}}$

(2) $\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}$

(3)  $\frac{\mathbf{1}}{\mathbf{2}}$

(4) $\frac{\mathbf{1}}{\mathbf{4}}$

Answer Key:
(4) $\frac{\mathbf{1}}{\mathbf{4}}$

$\frac{\mathbf{ }}{}$
17. Consider an ellipse whose centre is of the origin and its major axis is along x-axis. If its
eccentrcity is $\frac{\mathbf{3}}{\mathbf{5}}$ and the distance between its foci is 6, then the area of the quadrilateral
inscribed in the ellipse with diagonals as major and minor axis of the ellipse is
(1) 8 

(2) 32 

(3) 80 

(4) 40
Answer Key:
(4) 40

 
18. Area of the greatest rectangle inscribed in the ellipse  $\frac{{\mathbf{x}}^{\mathbf{2}}}{{\mathbf{a}}^{\mathbf{2}}}\mathbf{+}\frac{{\mathbf{y}}^{\mathbf{2}}}{{\mathbf{b}}^{\mathbf{2}}}$=1 is
(1) 2ab 

(2) ab 

(3) $\sqrt{\mathbf{a}\mathbf{b}}$

(4) $\frac{\mathbf{a}}{\mathbf{b}}$
Answer Key:
(1) 2ab

 
19. An ellipse hasOB as semi minor axes, F and F′ its foci and the angle FBF′ is a right angle.
Then the eccentricity of the ellipse is
(1) $\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$

(2) $\frac{\mathbf{1}}{\mathbf{2}}$

(3) $\frac{\mathbf{1}}{\mathbf{4}}$

(4) $\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}$

Answer Key:
(1) $\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$

$\frac{\sqrt{\mathbf{ }}}{}$
20. The eccentricity of the ellipse (x − 3)² + ( y − 4)² = $\frac{{\mathbf{y}}^{\mathbf{2}}}{\mathbf{9}}$ is
(1) $\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}$

(2) $\frac{\mathbf{1}}{\mathbf{3}}$

(3) $\frac{\mathbf{1}}{\mathbf{3}\sqrt{\mathbf{2}}}$

(4) $\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}$

Answer Key:

(2) $\frac{\mathbf{1}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
21. If the two tangents drawn from a point P to the parabola y²  = 4x are at right angles then the
locus of P is
(1) 2x +1 = 0 

(2) x = −1 

(3) 2x −1 = 0 

(4) x =1
Answer Key:
(2) x = −1 

 
22. The circle passing through (1,-2) and touching the axis of x at (3,0) passing through the point
(1) (-5,2) 

(2) (2,-5) 

(3) (5,-2) 

(4) (-2,5)
Answer Key:
(3) (5,-2) 

 
23. The locus of a point whose distance from (-2,0) is $\frac{\mathbf{2}}{\mathbf{3}}$ times its distance from the line x=$\frac{\mathbf{-}\mathbf{9}}{\mathbf{2}}$ is
(1) a parabola 

(2) a hyperbola 

(3) an ellipse 

(4) a circle
Answer Key:
(3) an ellipse 

 
24. The values of m for which the line y = mx + 2$\sqrt{\mathbf{5}}$ touches the hyperbola 16x² − 9y² =144 are
the roots of x² − (a + b)x − 4 = 0 , then the value of (a + b) is
(1) 2 

(2) 4 

(3) 0 

(4) -2
Answer Key:
(3) 0 

 
25. If the coordinates at one end of a diameter of the circle x² +y² −8x − 4y + c = 0 are (11, 2) ,
the coordinates of the other end are
(1) (-5,2) 

(2) (–3, 2) 

(3) (5,-2) 

(4) (-2,5)
Answer Key:
(2) (–3, 2) 

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics