Intercept Made by Circle on Axes

Q. Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

Q. A rod PQ of length 2a slides with its ends on the axes the locus of the circum-centre of $\Delta$ OPQ is

1. + = 4
2. + = 2
3. + = 3
4. + =

Q. Solve the system of inequalities graphically:

Q. The equation of perpendicular bisectors of the sidesAB and AC of a triangle ABC are x- y +5 = 0 and x + 2y =0 respectively. If the point A is (1, - 2), thenthe equation of line BC is

Q.

what is co-axial circle how to determine its equation and also tell its figure

Q. Find the equation of the circle with radius $5$ whose centre lies on $x$-axis and passes through the point $(2,3)$

Q. The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$, then equation of the hyperbola is
(a) x² + y² = 32
(b) x² − y² = 16
(c) x² + y² = 16
(d) x² − y² = 32

Q. A circle touches the x axis and also touches the circle with centre(0, 3) and radius 2. Find the lucid of the centre of circle?

Q.

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0, b). The reflection of O in the line AB is the point

1. $[\frac{2a{b}^2}{a^2+b^2},\frac{2a^{2}b}{a^2+b^2}]$
   

2. $[\frac{2a^{2}b}{a^2+b^2},\frac{2a{b}^2}{a^2+b^2}]$
   

3. $[\frac{2ab}{a^2+b^2},\frac{2ab}{a^2+b^2}]$
   

4. $(a,b)$