Question

Arrange in the descending order of the values:

$A$: If $(9,12)$ is one end of a focal chord of the parabola $y^2=16x$ then the slope of it is
$B$: The parabola $x^2=py$ passes through $(12,16)$, the focal distance of the point is
$C$: If the parabola $y^2=kx$ passes through $(9,6)$ then the value of $k$ is
$D$: The Ordinate of the point on the parabola $y^2=36x$ whose ordinate is three times its abscissa is

Write the value of the above statements in the descending order

• A. $B,D,C,A$
• B. $B,D,A,C$
• C. $D,B,C,A$
• D. $A,B,C,D$

Answer 1

The correct option is A $B,D,C,A$

We find the parameters option-wise.

A. Given parabola, $y^2=16x$. One end of focal chord is $(9,12)$

For the given parabola, focus is $(a,0)$

Comparing the given equation with a standard parabola we get, $a=4$

So now we have two points on the focal chord and we need its slope. So

$m=\frac{12-0}{9-4}=\frac{12}{5}$

B. Given parabola $x^2=py$

It passes through $(12,16)$ so putting these values in parabola equation we get, $p=9$

comparing it to a standard equation $x^2=4ay$ we see that $a=\frac{9}{4}$

Now focal distance of the given point is $a+y=\frac{9}{4}+12=\frac{57}{4}$

C. Given parabola $y^2=kx$

It should satisfy the given point $(9,6)$

Thus, $k=4$

D. Given parabola $y^2=36x$

Now ordinate is 3 times its abscissa so point is $(x,3x)$

Putting this in the equation of parabola we get, $x=4$ and $y=12$

So descending order is $B,D,C,A$