Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

find the eccentricity of the ellipse whose latusrectum makes rightangle at the centre?

find the eccentricity of the ellipse whose latusrectum makes rightangle at the centre?

Grade:10

1 Answers

Vikas TU
14149 Points
5 years ago
 

If the coordinates of the required point on the ellipse (1) be (√6 cos Φ, √2 sin Φ) then the tangent at the point is x/√6 cos Φ + y/√2 sin Φ = 1 ...... (2)

Slope of (2) = (-cos Φ)/√6 ×√2/(sin Φ ) = (-√2)/√6 cot Φ

As the tangents are equally inclined to the axes so we have

-1/√3 cot Φ = + tan 45o = + 1

Hence, tan Φ = + 1/√3

The coordinates of the required points are

(±√6 × √3/2, ±√2 × 1/2) and (±√6 × √3/2, ±√2 × 1/2)

= (± (3√2)/2, ±1/√2) and (± (3√2)/2, ± 1/√2)

Again the length of perpendicular from (0, 0) and (2),

= (√6.√2)/√(2 cos2Φ + 6 sin2Φ)

= (2√3)/√((2.3/4) + (6.1/4) )

= (2√3)/√3

= 2.

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free