Differential Equations Part 1

Let (h, k) be the vertex of parabola. Then, equation of parabola parallel to Y-axis is
(x−h)2=4a(y−k) ...(i)
Also,
Length of latusrectum = Distance of point (2, − 3) from the line
3x + 4y = 5
⇒4a=

|6−12−5|

√32+42

⇒4a=

11

5

∴ From Eq. (i),
(x−h)2=

11

5

(y−k)
Differentiating w.r.t. x, we get
2(x−h)=

11

5

dy

dx

Again, differentiating w.r.t. x
2=

11

5

d2y

dx2

⇒11

d2y

dx2

=10