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Question: If P(x<sub>1</sub>, y<sub>1</sub>) is a point on the ellipse b<sup>2</sup>x<sup>2</sup> + a<sup>2</s...

If P(x1, y1) is a point on the ellipse b2x2 + a2y2 = a2b2 then the area of DSPS¢ =

A

aea2−x12\sqrt{a^{2} - x_{1}^{2}}

B

beb2−x12\sqrt{b^{2} - x_{1}^{2}}

C

aeb2−x12\sqrt{b^{2} - x_{1}^{2}}

D

bea2−x12\sqrt{a^{2} - x_{1}^{2}}

Answer

bea2−x12\sqrt{a^{2} - x_{1}^{2}}

Explanation

Solution

x2a2\frac{x^{2}}{a^{2}} + y2b2\frac{y^{2}}{b^{2}} = 1 ̃ y12b2\frac{{y_{1}}^{2}}{b^{2}}= 1−x12a21 - \frac{{x_{1}}^{2}}{a^{2}}

y1 = a2−x12\sqrt{a^{2} - {x_{1}}^{2}}

DSPS¢ = 12\frac{1}{2}× 2ae × y1 = ae × a2−x12\sqrt{a^{2} - {x_{1}}^{2}}

DSPS¢ = be(a2−x12)\sqrt{\left( a^{2} - {x_{1}}^{2} \right)}