Question

Find the equations of both tangent lines to the ellipse x²/7 + y²/9 = 63 that pass through the point (21, 3). What is the question?

a) Determine the center of the ellipse.
b) Find the slope of the tangent lines.
c) Calculate the eccentricity of the ellipse.
d) Write the equation of the ellipse in standard form.

Answer 1

To find the equations of the tangent lines to the ellipse and pass through the point (21, 3), we can use the concept of the slope of the tangent line.

Step-by-step explanation:

To find the equations of the tangent lines to the ellipse and pass through the point (21, 3), we can use the concept of the slope of the tangent line.

First, we find the slope of the tangent line at the point of tangency on the ellipse by taking the derivative of the equation of the ellipse. Then, using the point-slope form of a line, we can find the equation of the tangent line.

Repeat the steps above for the second tangent line, considering the fact that a line perpendicular to the tangent line has a negative reciprocal slope.