Question

Let A and B are two fixed points in a plane then locus of another point C on the same plane then CA+CB = constant, \(>AB\) is

• A. circle
• B. ellipse
• C. parabola
• D. hyperbola

Hint:

Ellipse: sum of distances from two fixed points (foci) is constant and greater than distance between foci.

Answer 1

The Correct Option is B

Step 1: Recall definition of ellipse.
Ellipse is the locus of a point whose sum of distances from two fixed points (foci) is constant.
Step 2: Apply to given condition.
Given fixed points A and B and point C such that:
\[ CA + CB = \text{constant} \]
Also constant \(> AB\), which is necessary condition for ellipse to exist.
Step 3: Conclude.
Thus locus of C is an ellipse with foci at A and B.
Final Answer:
\[ \boxed{\text{Ellipse}} \]