Question

Where does the tangent touch in the ellipse?

• A. Long axis
• B. Short axis
• C. Focus
• D. Curve

Hint:

A tangent to an ellipse touches its curved boundary at one point, perpendicular to the radius at that point.

Answer 1

The Correct Option is D

Defining a tangent to an ellipse
Step 1: A tangent to an ellipse is a line that touches the ellipse at exactly one point, known as the point of tangency.
Identifying the point of contact
Step 2: The tangent touches the ellipse on its curve (the boundary of the ellipse), not specifically at the long axis, short axis, or focus, as these are geometric properties, not points of contact.
Evaluating options
Step 3: Analyze the options:
- (A) Long axis: Incorrect, as the long axis is a line through the ellipse, not a point.
- (B) Short axis: Incorrect, as the short axis is also a line.
- (C) Focus: Incorrect, as tangents do not necessarily touch at the foci.
- (D) Curve: Correct, as the tangent touches the ellipse’s curved boundary.
Thus, the correct answer is (D).