A tangent having slope -4/3 to the ellipse (x^2)/18 + (y^2)/32=1 intersects the major and minor axes at A and B. If O is the origin, then the area of…

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A tangent having slope -4/3 to the ellipse (x^2)/18 + (y^2)/32=1 intersects the major and minor axes at A and B. If O is the origin, then the area of ΔOAB is

MARKS Content Team · Accepted Answer

Correct answer: (C) 24 sq. units. Any point on the ellipse (x^2)/(32^2) + (y^2)/(42^2)=1 can be taken as 3√2cos⁡θ, 4√2sin⁡θ and the slope of the tangent as - (b^2x)/(a^2y) Hence, slope=- (323√2cos⁡θ)/(18 4√2sin⁡θ)=- 4/3cot⁡θ…. 1 Given, the slope of the tangent =-4/3…. 2 From equations (1) and (2), we get, cot⁡θ=1⇒θ=(π)/4 Hence, the equation of the tangent is x.1/(√2)3√2 + (y. 1)/(√2)4√2=1 (i.e.) x/6 + y/8=1 Hence, A=6, 0, B=0, 8 Area of ΔOAB=1/2× 6 × 8=24 sq. units

A tangent having slope $- \frac{4}{3}$ to the ellipse $\frac{x^{2}}{18} + \frac{y^{2}}{32} = 1$ intersects the major and minor axes at $A$ and $B$ . If $O$ is the origin, then the area of $Δ O A B$ is

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A tangent having slope -43 to the ellipse x218 + y232=1 intersects the major and minor axes at A and B. If O is the origin, then the area of ΔOAB is

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More Ellipse Questions

A tangent having slope $- \frac{4}{3}$ to the ellipse $\frac{x^{2}}{18} + \frac{y^{2}}{32} = 1$ intersects the major and minor axes at $A$ and $B$ . If $O$ is the origin, then the area of $Δ O A B$ is