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For all real p, the line 2px+ysqrt(1-p^(...

For all real p, the line `2px+ysqrt(1-p^(2))=1` touches a fixed ellipse whose axex are the coordinate axes
The locus of the point of intersection of perpendicular tangent is

A

`x^(2)+y^(2)=5//4`

B

`x^(2)+y^(2)=3//2`

C

`x^(2)+y^(2)=2`

D

none of these

Text Solution

AI Generated Solution

To solve the problem step by step, we will analyze the given line and the ellipse, and then find the locus of the point of intersection of the perpendicular tangents. ### Step 1: Understand the given line and its relation to the ellipse The line given is: \[ 2px + y\sqrt{1 - p^2} = 1 \] This line touches a fixed ellipse whose axes are the coordinate axes. ### Step 2: Write the standard form of the ellipse ...
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