List of top Mathematics Questions on Parabola asked in BITSAT

Let \(L_1\) be the length of the common chord of the curves \[ x^2 + y^2 = 9 \quad {and} \quad y^2 = 8x \] and let \(L_2\) be the length of the latus rectum of \(y^2 = 8x\). Then:

If the focus of the parabola \[ (y - k)^2 = 4(x - h) \] always lies between the lines \(x + y = 1\) and \(x + y = 3\) then:

What is the slope of the normal at the point (at, 2at) of the parabola y = 4ax ?

Consider the equation of a parabola $y^2 + 4ax = 0$, where $a > 0$ which of the following is/are correct?

The equation of one of the common tangents to the parabola $y^{2}=8 x$ and $x^{2}+y^{2}-$

Let $S$ be the focus of the parabola $y ^{2}=8 x$ and let $PQ$ be the common chord of the circle $x^{2}+y^{2}-2 x-4 y=0$ and the given parabola. The area of the $\Delta PQS$ is

Through the vertex $O$ of a parabola $y^2 = 4x$, chords $OP$ and $OQ$ are drawn at right angles to one another. The locus of the middle point of $PQ$ is

If the line $2x - 3y = k$ touches the parabola $y^2 = 6x$, then find the value of $k$.

The length of the latus rectum of the parabola $169\left[(x-1)^{2}+(y-3)^{2}\right]=(5 x-12 y+ 17) ^{2}$ is:

If $2x + 3y + 12 = 0$ and $x - y + 4 \lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$, then $\lambda$ is equal to

The equation of a parabola which passes through the intersection of a straight line $x + y = 0$ and the circle $x^2 + y ^2 + 4y = 0$ is :