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Chapter 10: Q. 77 (page 645)

Show that an equation of the form Cy2+Dx=0where C,D are not equat to 0 is the equation of a parabola with vertex at 0,0and axis

of symmetry the x-axis. Find its focus and directrix.

Short Answer

Expert verified

The focus is -D4C,0and directrix isx=D4C.

Step by step solution

01

Step 1. Given information .

Consider the given equation and vertex .

02

Step 2.  Standard form of parabola used .

The standard form of parabola isy-k2=4ax-hwhere h , k are the points of center and x , y are the points of focus .

03

.  Find the equation .

To find the equation of parabola rewrite the given equation in the standard form .

y-02=4-D4Cx-0

Compare this equation with standard form .

a=-D4C

Since the value of a=-D4C,then the focus is 0+a,0=-D4C,0and the directrix is x=h-a=D4C.

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