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

Question 1.

Prove that liney = x+ \(\sqrt { (5/6) }\) touches ellipse 2x^{2} + 3y^{2} = 1. Also find the coordinates of tangent point.

Solution:

Question 2.

Show that line x – 3y – 4 = 0 touches ellipse 3x^{2} + 4y^{2} = 20.

Solution:

Equation of line, x – 3y – 4 =0

⇒ x = 3y + 4

Equation of ellipse,

3x^{2} + 4y^{2} = 20

Putting value of x from (i) in eqn. (ii),

3(3y + 4)^{2} + 4y^{2} = 20

⇒ 3(9y^{2} + 24y + 16) + 4y^{2} – 20 = 0

⇒ 27y^{2} + 72y + 48 + 4y^{2} – 20 = 0

⇒ 31y^{2} + 72y + 28 = 0

Line will touch eq^{n}. (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 5x^{2} + 4y^{2} = 20.

Solution:

Equation of line,

3x – 4y = k

⇒ 3x – k = 4y

⇒ 4y = 3x – k

Question 4.

Prove that line

touches ellipse

Also find the coordinates of tangent point.

Solution:

Question 5.

Find the condition that line lx + my = n touches the ellipse

Solution:

Question 6.

Find the equations of tangent for ellipse 4x^{2} + 3K^{2} = 5 which makes equation angle of 60° with x-axis. Also find the coordinates of tangent point.

Solution:

Equation of ellipse

4x^{2} + 3y^{2} = 5

## Leave a Reply