Question

Find the equation of the parabola whose
Focus is 3 (3,5) and vester A (1,3)​

Answer 1

S

Find the equation of the parabola whose focus is S(3,5) and vertex is A(1,3).

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ANSWER

Slope of axis=

3−1

5−3

=

2

2

=1

Slope of directrix=−1

equation of tangent at vertex A

Pt(1,3),m=−1

⇒y−3=−1(x−1)

⇒x+y−4=0

equation of directrix

x+y=λ

a=SA

=

4+4

=2

2

A is midpoint of PS

2

n+3

=1,

2

k+5

=3

⇒n=−1,k=1

(−1,1) lies on directrix

−1+1=λ=0

equation of diectrix: L:y+x=0

QO=QS

⇒

∣

∣

∣

∣

2

l+m

∣

∣

∣

∣

=

(l−3)

2

+(m−5)

2

⇒(l+m)

2

=2[(l−3)

2

+(m−5)

2

]

⇒(x+y)

2

=2[(x−3)

2

+(y−5)

2

]

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