The circles x^2+y^2-x-y=0 and x^2+y^2-x+y=0 intersect at an angle (a) (π)/(2) (b) (π)/(3) (c) (π

step 1 In this question we are provided with equation of two circles. First circle is x square plus y s

The circles x^2+y^2-x-y=0 and x^2+y^2-x+y=0 intersect at an...

Key Concepts

Circle Equation and Center-Radius Form

A circle in the Cartesian plane is generally described by an equation that can be rewritten into a standard form, (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r its radius. This form is foundational in understanding the circle's geometric properties and in solving problems involving circles.

Completing the Square

Completing the square is a technique used to transform a quadratic expression into a perfect square plus or minus a constant. In the context of circle equations, it is used to convert the general quadratic form into the standard center-radius form, revealing the center and radius of the circle, which are essential for geometric analysis.

Angle Between Curves

The angle at which two curves intersect is defined by the angle between their tangent lines at the point of intersection. This concept is important for understanding how curves, including circles, interact with one another and provides a method to quantify the 'sharpness' of the intersection.

Tangent Lines to Curves

A tangent line to a curve at a given point is a straight line that touches the curve only at that point and has the same slope as the curve there. In problems involving the intersection of circles, finding the tangent lines is crucial in determining the angle of intersection, as these tangents represent the instantaneous direction of the curves at the point of contact.

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