Question:medium

The line ax+by=1 cuts ellipse cx²+dy²=1 only once if

Show Hint

Tangency gives discriminant zero condition.

Updated On: Mar 18, 2026

ca²+db²=1
(c)/(a²)+(d)/(b²)=1
(a²)/(c)+(b²)/(d)=1
a²c+b²d=1

Show Solution

The Correct Option is C

Solution and Explanation

Was this answer helpful?

0

Top Questions on sections of a cone

Let P be a point on the parabola, \( x^2 = 4y \). If the distance of P from the centre of the circle, \( x^2 + y^2 + 6x + 8 = 0 \) is minimum, then the equation of the tangent to the parabola at P, is :
- BITSAT - 2026
- Mathematics
- sections of a cone
View Solution
If two tangents from point \((h,k)\) to parabola \(y^2 = 64x\) have slopes such that one is 8 times the other, then value of \( \frac{k^2}{2h} \) is:
- MET - 2024
- Mathematics
- sections of a cone
View Solution
The eccentricity of the conic \(9x^2 - 16y^2 = 144\) is
- MET - 2021
- Mathematics
- sections of a cone
View Solution
The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity would be
- BITSAT - 2021
- Mathematics
- sections of a cone
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in BITSAT exam

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is:

BITSAT - 2026
Relative Velocity

If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :

BITSAT - 2026
Definite Integral

If \( x = \sqrt{2^{\text{cosec}^{-1} t}} \) and \( y = \sqrt{2^{\text{sec}^{-1} t}} (|t| \ge 1) \), then dy/dx is equal to :

BITSAT - 2026
Derivatives of Functions in Parametric Forms

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately 0.530 \AA. The radius for the first excited state (n = 2) orbit is (in \AA)

BITSAT - 2026
Bohr's model of hydrogen atom