Question

The vertex of a parabola is (a,0) and the directrix is x+y = 3a. The equation of the parabola is (a) x² + 2xy + y2 + ax + 10ay + 7a² = 0 (6) x² - 2xy + y2 + 6ax + 10ay = 7a (c) x2 – 2xy + y2 - 6ax + 10ay = 7a (d) None of these​

Answer 1

Answer:

Solution

verified

Verified by Toppr

Correct option is A)

Equation of axis is given by, x−y=c, since the directrix and axis of the parabola are perpendicular to each other.

It also passes through vertex (a,0)⇒c=a

Now solving directrix and axis to get foot of directrix. x=2a,y=a

We know vertex is mid point of foot of directrix and focus. ∴

focus is S(0,−a)

Now using definition of parabola,

PS

2

=PM

2

⇒(x−0)

2

+(y+a)

2

=(

2

x+y−3a

)

2

⇒2(x

2

+y

2

+2ay+a

2

)=x

2

+y

2

+9a

2

+2xy−6ax−6ay

⇒x

2

+y

2

−2xy+6ax+10ay−7a

2

=0