The locus of the middle points of the focal chords of parabola, y2=8 x is another parabola whose length of latus rectum is

Question

The locus of the middle points of the focal chords of parabola, y2=8 x is another parabola whose length of latus rectum is (A) 1 (B) 2 (C) 3 (D) 4

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e44917e5bfd260b6adb962c38c340c6b-.png" /> 2 h = a ( t 12+ t 22) ldots(1) text and 2 k =2 a ( t 1+ t 2)....(2) text and t 1 t 2=-1 text from (2) k 2= a 2[(2 h / a )-2] y 2=2 a ( x -2 a ) text Put a =2 text Hence, y 2=4( x -4)

Q. The locus of the middle points of the focal chords of parabola, $y^{2} = 8 x$ is another parabola whose length of latus rectum is

1

2

3

4

$2 h = a (t_{1}^{2} + t_{2}^{2}) \dots (1)$
$and 2 k = 2 a (t_{1} + t_{2})$ ....(2)
$and t_{1} t_{2} = - 1$
$from (2)$
$k^{2} = a^{2} [\frac{2 h}{a} - 2]$
$y^{2} = 2 a (x - 2 a)$
$Put a = 2$
$Hence, y^{2} = 4 (x - 4)$

Q. The locus of the middle points of the focal chords of parabola, y2=8x is another parabola whose length of latus rectum is

1

2

3

4

2h=a(t12​+t22​)…(1) and 2k=2a(t1​+t2​)....(2) and t1​t2​=−1 from (2) k2=a2[a2h​−2] y2=2a(x−2a) Put a =2 Hence, y2=4(x−4)

Q. The locus of the middle points of the focal chords of parabola, $y^{2} = 8 x$ is another parabola whose length of latus rectum is

$2 h = a (t_{1}^{2} + t_{2}^{2}) \dots (1)$
$and 2 k = 2 a (t_{1} + t_{2})$ ....(2)
$and t_{1} t_{2} = - 1$
$from (2)$
$k^{2} = a^{2} [\frac{2 h}{a} - 2]$
$y^{2} = 2 a (x - 2 a)$
$Put a = 2$
$Hence, y^{2} = 4 (x - 4)$