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Question

Mathematics Question on Conic sections

Locus of the image of the point (2,3)(2, 3) in the line (2x−3y+4)+k(x−2y+3)=0,k∈R,\left(2x - 3y + 4\right) + k\left(x - 2y + 3\right) = 0, k \in R, is a

A

Straight line parallel to x-axis

B

Straight line parallel to y-axis

C

Circle of radius 2\sqrt{2}

D

Circle of radius 3\sqrt{3}

Answer

Circle of radius 2\sqrt{2}

Explanation

Solution


PR=RQP R=R Q
(x−1)2+(y−2)2=(2−1)2+(3−2)2(x-1)^{2}+(y-2)^{2}=(2-1)^{2}+(3-2)^{2}
(x−1)2+(y−2)2=2(x-1)^{2}+(y-2)^{2}=2