What will be the length of the longest chord of a circle that passes through the point (-1,0) and touches - Maths - Vector Algebra

Question

What will be the length of the longest chord of a circle that
passes through the point (-1,0) and touches the y-axis at (0,2) ?

Aarushi Mishra · Accepted Answer

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Let center of circle be C
Since y axis is tangent to the circle therefore the line joining center and point of tangency will be perpedicular to the y axis, CB is perpendicular to y axis and thus parallel to x axis, therefore y co-ordinate of center will be 2 see fig
Let co-ordinates of C=a,2Radius, r=CB=aEquation of circle with center C and radius ax-a2+y-22=a2x2+a2-2ax+y2+4-4y=a2x2+y2-2ax-4y+4=0Circle passes through -1,0, it must satisfy the equation1+0+2a+4=0a=-52Longest chord is the diameter of circleLength of diameter=2r=2a=2-52=5

What will be the length of the longest chord of a circle that passes through the point (-1,0) and touches the y-axis at (0,2) ?