Exams Joint Entrance Examination Mathematics Ellipse Question 147 Question 147 of 183 Medium MCQ
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 :
Solutions · 1 Post your solution Official solution
3 x 2 + 5 y 2 = 32 3{x^2} + 5{y^2} = 32 3 x 2 + 5 y 2 = 32
6x + 10yy' = 0
\[ \Rightarrow y' = {{ - 3x} \over {5y}}\]
\[ \Rightarrow y{'_{(2,2)}} = - {3 \over 5}\]
Tangent \[(y - 2) = - {3 \over 5}(x - 2) \Rightarrow Q\left( {{{16} \over 3},0} \right)\]
Normal \[(y - 2) = {5 \over 3}(x - 2) \Rightarrow R\left( {{{4} \over 5},0} \right)\]
\[ \therefore \] Area = \[{1 \over 2}(QR) \times 2 = QR = {{68} \over {15}}\] Answer the question to unlock