Locus of the middle point of chords of parabola y2=4 x, tangents drawn at the ends of which intersect at right angle is a parabola whose

Question

Locus of the middle point of chords of parabola y2=4 x, tangents drawn at the ends of which intersect at right angle is a parabola whose (A) vertex is (1,0) (B) length of shortest focal chord is 2 (C) equation of directrix is x=(1/2) (D) tangents at ends of latus-rectum intersect at ((1/2), 0)

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5634060b4830419c9f38232e59a664e6-.png" /> To find locus of the middle point of all focal chords T = S 1 yk -2( x + h )= k 2-4 h passes through (1,0) -2(1+h)=k2-4 h Hence, locus is y 2=2 x -2=2( x -1). Now, verify alternatives.

Q. Locus of the middle point of chords of parabola $y^{2} = 4 x$ , tangents drawn at the ends of which intersect at right angle is a parabola whose

vertex is $(1, 0)$

length of shortest focal chord is 2

equation of directrix is $x = \frac{1}{2}$

tangents at ends of latus-rectum intersect at $(\frac{1}{2}, 0)$

To find locus of the middle point of all focal chords
$T = S_{1}$
$y k - 2 (x + h) = k^{2} - 4 h$ passes through $(1, 0)$
$- 2 (1 + h) = k^{2} - 4 h$
Hence, locus is $y^{2} = 2 x - 2 = 2 (x - 1)$ .
Now, verify alternatives.

Q. Locus of the middle point of chords of parabola y2=4x, tangents drawn at the ends of which intersect at right angle is a parabola whose

vertex is (1,0)

length of shortest focal chord is 2

equation of directrix is x=21​

tangents at ends of latus-rectum intersect at (21​,0)

To find locus of the middle point of all focal chords T=S1​ yk−2(x+h)=k2−4h passes through (1,0) −2(1+h)=k2−4h Hence, locus is y2=2x−2=2(x−1). Now, verify alternatives.

Q. Locus of the middle point of chords of parabola $y^{2} = 4 x$ , tangents drawn at the ends of which intersect at right angle is a parabola whose

vertex is $(1, 0)$

equation of directrix is $x = \frac{1}{2}$

tangents at ends of latus-rectum intersect at $(\frac{1}{2}, 0)$

To find locus of the middle point of all focal chords
$T = S_{1}$
$y k - 2 (x + h) = k^{2} - 4 h$ passes through $(1, 0)$
$- 2 (1 + h) = k^{2} - 4 h$
Hence, locus is $y^{2} = 2 x - 2 = 2 (x - 1)$ .
Now, verify alternatives.