If the tangent at a point P on the parabola y^2=3x is parallel to the line x+2y=1 and the tangents at the points Q and R on the ellipse x^24+ y^21=1 are perpendicular to the line x-y=2 , then the are…

Question

If the tangent at a point P on the parabola y^2=3x is parallel to the line x+2y=1 and the tangents at the points Q and R on the ellipse x^24+ y^21=1 are perpendicular to the line x-y=2 , then the area of the triangle PQR is

Accepted Answer

Correct answer: D. (d) Solution y^2=3x Tangent P (x_1 ,y_1 ) is parallel to x+2y=1 Then slope at P=- 12 2y dy dx=3 ⇒ dy dx= 32y=- 12 ⇒y_1=-3 Coordinates of P (3 ,-3 ) similarly Q ( 4 3 , 1 5 ) ,R(- 4 5 , -1 5) Area of ∆ PQR = 12(3-31 4 5 1 51- 4 5- 1 51) = 12(3 ( 2 5 )+3 ( 8 5 )+0)= 302 5=3 5

$If the tangent at a point P on the parabola y^{2} = 3 x is parallel to the line x + 2 y = 1 and the tangents at the points Q and R on the ellipse \frac{x ^{2}}{4} + \frac{y ^{2}}{1} = 1 are perpendicular to the line x - y = 2, then the area of the triangle PQR is$

Solution

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