Let O be the vertex of the parabola = 4y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2: 3 be the conic C. [2026]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Let O be the vertex of the parabola $x^{2}$ = 4y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2 : 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is: [2026]

1 $4 x - 5 y + 6 = 0$

2 $x - 2 y + 3 = 0$

3 $5 x - 4 y + 3 = 0$

4 $5 x - y - 3 = 0$

Ans.
(3)

$h = \frac{4 t}{5}$

$k = \frac{2 t^{2}}{5} = \frac{2}{5} {(\frac{5 h}{4})}^{2}$

$8 k = 5 h^{2}$

$\Rightarrow 5 x^{2} = 8 y$

$T = S_{1}$

$5 (x x_{1}) - 4 (y + y_{1}) = 5 x_{1}^{2} - 8 y_{1}$

$5 x - 4 (y + 2) = 5 - 8 \cdot 2$

$5 x - 4 y + 3 = 0$

Want Us to Email you About Special Offers & Updates?