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Let the line $y = m x$ and the ellipse $2 x^{2} + y^{2} = 1$ intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co–ordinate axes at $(- \frac{1}{3 \sqrt{2}}, 0)$ and $(0, β)$ , then $β$ is equal to:

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Correct option is B

Let P be x1,y1Equation of normal at P isx2x1−yy1=−12It passes through −132,0 ⇒ −162x1=−12 ⇒ x1=132 So y1=223(as P lies in 1st quadrant) ,β=y12=23

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Let the line y=mx and the ellipse 2x2+y2=1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co–ordinate axes at −132,0 and 0,β, then βis equal to:

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Ready to Test Your Skills?

free study material

Let the line $y = m x$ and the ellipse $2 x^{2} + y^{2} = 1$ intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co–ordinate axes at $(- \frac{1}{3 \sqrt{2}}, 0)$ and $(0, β)$ , then $β$ is equal to: