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Maths-

General

Easy

Question

Statement-1: The distance of the tangent through (0, (d) from a focus of the ellipse $fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 7 end fraction equals 1$ is 5
and
Statement-2: The locus of the foot of the perpendicular from a focus on any tangent to $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ is $x to the power of 2 end exponent plus y to the power of 2 end exponent equals a to the power of 2 end exponent$

Statemetn-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
Statement-1 is True, Statement-2 is False
Statement-1 is False, Statement-2 is True.

The correct answer is: Statemetn-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

$e equals square root of fraction numerator a to the power of 2 end exponent minus b to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction end root equals square root of fraction numerator 9 over denominator 16 end fraction end root equals fraction numerator 3 over denominator 4 end fraction$
A focus is (3, 0)
(0, (d) is a point on $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 16$
It is the foot of the perpendicular from the focus on the tangent
Required distance = $square root of left parenthesis 0 minus 3 right parenthesis to the power of 2 end exponent plus left parenthesis 4 minus 0 right parenthesis to the power of 2 end exponent end root equals 5$

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