P (–1, 4) is a point on a circle, centre O which is at the origin. Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c

A tangent makes an angle of 90 degrees with the radius of a circle.Using this fact, we find the gradient of the radius going through P = -4Therefore gradient of the tangent to the circle at P is -1/-4 = 1/4Then use equation for a straight line: y - y1 = m(x-x1) where x1 and y1 are the x and y coordinates of P respectively (-1,4)So we get that y = (1/4) x + 17/4