JEE MATHEMATICS MCQ: ELLIPSE

1 Hard

1 of 1

Analyzing +4 | -1

The locus of the mid-points of chords of the ellipse

\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1

that touch the circle

{x^2} + {y^2} = {b^2},

View answer and explanation

Correct option: B

{\left( {\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}} \right)^2} = {b^2}\left( {\frac{{{x^2}}}{{{a^4}}} + \frac{{{y^2}}}{{{b^4}}}} \right)

Option B

{\left( {\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}} \right)^2} = {b^2}\left( {\frac{{{x^2}}}{{{a^4}}} + \frac{{{y^2}}}{{{b^4}}}} \right)

is correct because it represents the locus of the midpoints of chords of the ellipse that touch the given circle.

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