JEE PYQ: Ellipse Question 4
Question 4 - 2021 (26 Feb Shift 2)
Let $L$ be a common tangent line to the curves $4x^2 + 9y^2 = 36$ and $(2x)^2 + (2y)^2 = 31$. Then the square of the slope of the line $L$ is:
Type: Numerical
Show Answer
Answer: 3
Solution
$E: \frac{x^2}{9} + \frac{y^2}{4} = 1$, $C: x^2 + y^2 = \frac{31}{4}$
Equation of tangent to ellipse is $y = mx \pm \sqrt{9m^2 + 4}$
Equation of tangent to circle is $y = mx \pm \sqrt{\frac{31}{4}m^2 + \frac{31}{4}}$
Comparing: $9m^2 + 4 = \frac{31}{4}m^2 + \frac{31}{4}$
$\Rightarrow 36m^2 + 16 = 31m^2 + 31$
$\Rightarrow 5m^2 = 15$
$\Rightarrow m^2 = 3$
BETA
