JEE PYQ: Ellipse Question 21
Question 21 - 2019 (10 Apr Shift 2)
The tangent and normal to the ellipse $3x^2 + 5y^2 = 32$ at the point $P(2, 2)$ meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is:
(a) $\frac{34}{15}$ (b) $\frac{14}{3}$ (c) $\frac{16}{3}$ (d) $\frac{68}{15}$
Show Answer
Answer: (d) $\frac{68}{15}$
Solution
Tangent at P: $\frac{3x}{16} + \frac{5y}{16} = 1 \Rightarrow Q = \left(\frac{16}{3}, 0\right)$
Normal at P: $R = \left(\frac{4}{5}, 0\right)$
Area $= \frac{1}{2} \cdot |QR| \cdot 2 = \frac{68}{15}$
BETA
