RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6

Rajasthan Board RBSE Class 11 Maths Chapter 12 Conic Section Ex 12.6

Question 1.
Prove that liney = x+ \(\sqrt { (5/6) }\) touches ellipse 2x2 + 3y2 = 1. Also find the coordinates of tangent point.
Solution:
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6

Question 2.
Show that line x – 3y – 4 = 0 touches ellipse 3x2 + 4y2 = 20.
Solution:
Equation of line, x – 3y – 4 =0
⇒ x = 3y + 4
Equation of ellipse,
3x2 + 4y2 = 20
Putting value of x from (i) in eqn. (ii),
3(3y + 4)2 + 4y2 = 20
⇒ 3(9y2 + 24y + 16) + 4y2 – 20 = 0
⇒ 27y2 + 72y + 48 + 4y2 – 20 = 0
⇒ 31y2 + 72y + 28 = 0
Line will touch eqn. (ii) if
(72)2 – 4(31 )(28) = 0
∴ (72)2 – 4 × 31 × 28 = 5184 – 3472
= 1712 ≠ 0
Thus, given line will not be touch given ellipse.
∴ Given equation is wrong.

Question 3.
For which value of k, the line 3x – 4y = k touches the ellipse 5x2 + 4y2 = 20.
Solution:
Equation of line,
3x – 4y = k
⇒ 3x – k = 4y
⇒ 4y = 3x – k
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6

Question 4.
Prove that line
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6
touches ellipse
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6
Also find the coordinates of tangent point.
Solution:
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6

Question 5.
Find the condition that line lx + my = n touches the ellipse
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6
Solution:
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6

Question 6.
Find the equations of tangent for ellipse 4x2 + 3K2 = 5 which makes equation angle of 60° with x-axis. Also find the coordinates of tangent point.
Solution:
Equation of ellipse
4x2 + 3y2 = 5
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6
RBSE Solutions for Class 11 Maths Chapter 12 Conic Section Ex 12.6

RBSE Solutions for Class 11 Maths