Q128 / 225 · JEE Main 2004 · Mathematics

If $a \neq 0$ and the line $2 b x+3 c y+4 d=0$ passes through the points of intersection of the parabolas $y^2=4 a x$ and $x^2=4 a y$, then

Correct answer
A
$d^2+(2 b+3 c)^2=0$
B
$d^2+(3 b+2 c)^2=0$
C
$d^2+(2 b-3 c)^2=0$
D
$d^2+(3 b-2 c)^2=0$

Solution

Points of intersection of given parabolas are $(0,0)$ and $(4 a, 4 a)$ $\Rightarrow$ equation of line passing through these points is $y=x$ On comparing this line with the given line $2 b x+3 c y+4 d=0$, we get $d=0$ and $2 b+3 c=0 \Rightarrow(2 b+3 c)^2+d^2=0$

Hence, the correct answer is option: 'A'.

More Parabola Questions

Let a line perpendicular to the line touch the parabola at the point . The distance of the point from the centre of the circle is __________05 Apr, 2024 (E)Line and parabola
Let O be the vertex of the parabola and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segm08 Apr, 2026 (E)Locus
Let chord PQ of length of the parabola be such that the ordinates of points and are in the ratio . If the chord PQ subtends an angle at the 06 Apr, 2026 (M)Chord of parabola
Let the point be the vertex of the parabola . If a line passing through the point intersects the circle at the points and , then the maximum05 Apr, 2026 (E)standard equation of parabola
Let the directrix of the parabola , cut -axis at the point . Let , , be a point on such that the slope of is . If is a focal chord of , then05 Apr, 2026 (E)standard equation of parabola
Consider the parabola and the ellipse . Let the line segment joining the points of intersection of and , be their latus rectums. If the ecce04 Apr, 2026 (M)standard equation of parabola