The circle `x^2+y^2-4x-4y+4=0` is inscribed in a variable triangle `O A Bdot` Sides `O A` and `O B` lie along the x- and y-axis, respectively, where `O` is the origin. Find the locus of the midpoint of side `A Bdot`

If O is the origin and Q is a variable point on y^(2)=x* Find the locus of the mid point of OQ

If O is the origin and Q is a variable points on x^(2)=4y. Find the locus of the mid pint of OQ .

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

A line passing through P(4,2) meet the X and Y -axes at A and B, respectively.If O is the origin,then locus of the centre of the circumference of triangle OAB is

If the circle x^(2)+y^(2)-2x-2y+1=0 is inscribed in a triangle whose two sides are axes and one side has negative slope cutting intercepts a and b on x and y axis.Then

A circle x^(2)+y^(2)-2ax+2y=0 cuts the axis of x at the point A and it circumscribesan equilateral triangle with OA as one of its sides, where O is the origin.Find the value of a and theertices of the equilateral triangle.

Suppose OABC is a reatangle in the xy-plane where O is the origin and A, B lie on the parabola y=x^2) .

The circle x^(2)+y^(2)-4x-4y+4=0 is inscribed in a triangle which has two of its sides along the coordinate axes.The locus of the circumcenter of the triangle is x+y-xy+k(x^(2)+y^(2))^((1)/(2))=0. Find k

Let O be the origin and A be a point on the curve y^(2)=4x .Then locus of midpoint of OA is

The circle x^(2)+y^(2)-4x-4y+4=0 isinscribed in a traingle which has two sides alonthe coordianates axes.The locus of thecircumcentre of the triangle is x+y-xy+m sqrt(x^(2)+y^(2))=0. Then m is equal to