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The line `y = x` is an axis of symmetry for the circlesThe circles intersect at the origin and a point, P(say), which lies on the line `y = x`The line `y = x` is the radical axis of the pair of circles. The circles are orthogonal for all `a ne b`.

Answer :

A::B::CSolution :

Interchanging x and y in one equation gives the other equation. So, (a) is true, <br> Clearly (0,0) satisfies both circles and `y = x` is radical axis. So (b) and (c ) are true. The centres are (a,b) and (b,a) the radii are both `sqrt(a^(2)+b^(2))`. The distance between the centres `= |a-b| sqrt(2)` <br> If circles are orthogonal, `|a-b| sqrt(2) = 2(a^(2)+b^(2))` <br> Now, `2(a^(2)+b^(2)) ne 2(a^(2)-b^(2))`, for all a and b. Thus, (d) is false. **Standard equation of circle**

**General Equation of Circle When the circle passes through the origin.**

**General Equation of Circle When the circle touch x axis and y axis .**

**General Equation of Circle When the circle touches both the axis.**

**Important points to remember**

**Find the Equation; radius; center of the circle and its x intercept and y intercept ?**

**Theorem:- Prove that the equation `x^2+y^2+2gx+2fy+c=0` always represent a circle whose centre is `(-g;-f)` and radius `sqrt(g^2+f^2-c)`**

**Diameter form of the circle**

**Parametric form of circle**

**Equation of a circle passing through 3 points**