1. Tardigrade
  2. Question
  3. Mathematics
  4. The tangent and normal to the ellipse 3x2 + 5y2 = 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 :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 :

JEE MainJEE Main 2019Conic Sections

Solution:

$3x^2 + 5y^2 =32$
$\frac{dy}{dx} \Bigg|_{(2,2)} = - \frac{3}{5}$
Tangent $y-2 = - \frac{3}{5}\left(x-2\right) \Rightarrow Q\left(\frac{16}{3} ,0\right) $
Normal : $ y-2 = \frac{5}{3} \left(x-2\right) \Rightarrow R \left(\frac{4}{5},0\right) $
Area is $=\frac{1}{2}\left(QR\right)\times2 = QR = \frac{68}{15} $