Question is:

Let (c,d) be a point on the circle with the equation x^2+y^2=a^2 (c can not equal a or 0)

a) Find d in terms of a and c.

b) Find the equation of the tangent to the circle at (c,d) in terms of c and d.

- Posted:
- 3+ months ago by Nxc13
- Topics:
- circle, point, let s, question, math, equal, maths, equations

Details:

Question is:

Let (c,d) be a point on the circle with the equation x^2+y^2=a^2 (c can not equal a or 0)

a) Find d in terms of a and c.

b) Find the equation of the tangent to the circle at (c,d) in terms of c and d.

This is just a matter of rearranging the equation. You are supposed to be perfectly prepared in that before you get to this stage of the subject.

Given:

x^2 + y^2 = a^2 Substitute c and d.

c^2 + d^2 = a^2 The rule is you can do any valid operation on both sides of an equation and it will still be equal. Subtract c^2.

d^2 = a^2 - c^2 Square root.

d = √(a^2 - c^2) This identifies four points, (±c, ±d).

The tangent is defined as d/c when the circle is centered on the origin.