"If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of radius r, then r is equal to :"

Question

Accepted Answer

"Let P(h, k) and point on the circle is (cos$\theta$, sin$\theta$)

$\therefore$ ${{3 + \cos \theta } \over 2} = h$ and ${{2 + \sin \theta } \over 2} = k$

cos$\theta$ = 2h $-$ 3 and sin$\theta$ = 2h $-$ 2

Squaring and adding we get

${(2h - 3)^2} + {(2h - 2)^2} = 1$

$\Rightarrow 4{x^2} - 12x + 9 + 4{y^2} - 8y + 4 = 1$

$\Rightarrow 4{x^2} + 4{y^2} - 12x - 8y + 12 = 0$

$\Rightarrow {x^2} + {y^2} - 3x - 2y + 3 = 0$

Radius = $\sqrt {{9 \over 4} + 1 - 3} = {1 \over 2}$"

If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x² + y² = 1 is a circle of radius r, then r is equal to :

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If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of radius r, then r is equal to :

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If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x² + y² = 1 is a circle of radius r, then r is equal to :