Question 1099730

Find the equation of the line tangent to the circle x2 + y2 = 25 at point (3,4)
<pre>Calculus is UNNECESSARY here. How many people who ask questions on here know calculus? Help these people with the SIMPLEST steps so they can understand.

Looking at the the equation of the circle, the center is located at the origin, or at coordinate point: (0, 0). With the point of tangency being (3, 4), the slope of the radius line is: {{{4/3}}}
Now, as a tangent and radius line intersect at a perpendicular point, it follows that the tangent line's slope is {{{- 3/4}}}.
With the tangent line's point of (3, 4), and a slope of {{{- 3/4}}}, we use the point-slope form, or {{{matrix(1,3, y - y[1], "=", m(x - x[1]))}}} to find the equation of the tangent line
{{{matrix(1,3, y - 4, "=", (- 3/4)(x - 3))}}}
{{{matrix(1,3, y - 4, "=", (- 3/4)x + 9/4)}}}
{{{matrix(1,3, y, "=", (- 3/4)x + 9/4 + 16/4)}}}
{{{highlight_green(matrix(1,3, y, "=", (- 3/4)x + 25/4))}}}