Question

The locus of the point of intersection of the perpendicular tangents to ellipse x²/9 + y²/4 = 1 is

A. x² + y² = 4
B. x² + y² = 9
C. x² + y² =5
D. x² + y² = 13

Answer 1

The locus of the point of intersection of the perpendicular tangents to the ellipse x²/9 + y²/4 = 1 is x² + y² = 5.

Step-by-step explanation:

The locus of the point of intersection of the perpendicular tangents to the ellipse x²/9 + y²/4 = 1 is x² + y² = 5.

To find the locus of the point of intersection, we need to consider the equation of the ellipse and find the equations of the perpendicular tangents. The equation of the ellipse is given as x²/9 + y²/4 = 1.

To find the equations of the perpendicular tangents, we differentiate the equation of the ellipse with respect to x and solve for dy/dx. We then use the negative reciprocal of dy/dx to find the slope of the perpendicular tangents. Finally, we use the point-slope form of a line to find the equations of the perpendicular tangents.

By solving the equations of the perpendicular tangents, we get the equation of the locus of the point of intersection as x² + y² = 5.