Question

A variable circle passes through the fixed point
A(p, q) and touches x-axis. The locus of the other
end of the diameter through 'A' is

Answer 1

Answer:

touches the x-axis. Show that the locus of the other end of the diameter through A is (x-a)^2=4b ydot. ... A variable circle passes through the fixed `A (p, q)` and. play. 3 :29

Answer 2

Correct Answer:

A) (x−p)2=4qy

Description for Correct answer:

In a circle AB is as a diameter where the coordinate of A is (p, q) and let the co-ordinate at B is (x1, y1).

Equation of circle in diameter from is

(x−p)(x−x1)+(y−q)(y−y1)=0

x2−(p+x1)x+px1+y2 −(y1+q)y+qy1=0

x2−(p+x1)x+y2− (y1+q)y+px1+qy1=0

Since, the circle touches x-axis.

∴y=0

=> x2−(p+x1)x+px1+qy1=0

Also, the discriminant of above equation will be equal to zero because circle touches x-axis

∴(p+x1)2=4(px1+qy1) =>p2+x21+2px1=4px1+4qy1

=> x21−2px1+p2=4qy1

Therefore the locus of point B is (x−p)2=4qy