Find the equation of locus of a point p which divides a segment aq internally i the ratio 2:5,where
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Step-by-step explanation:
α=
5+2
2x+5(3)
;β=
5+2
2y+5(−2)
\alpha=\dfrac{2x+15}{7} ; \beta=\dfrac{2y-10}{7}α=
7
2x+15
;β=
7
2y−10
+10}{2}}x
x=
2
7α−15
;y=
2
7β+10
...(1)
x^2+y^2-4x-12=0x
2
+y
2
−4x−12=0
\boxed{\Rightarrow (x-2)^2+y^2=16}
⇒(x−2)
2
+y
2
=16
...(2)
Using (1) and (2)
\left(\dfrac{7 \alpha -15}{2}-2\right)^2+\left(\dfrac{7\beta +10}{2}\right)^2=16(
2
7α−15
−2)
2
+(
2
7β+10
)
2
=16
\left(\dfrac{1 \alpha -19}{2}\right)^2 +\left(\dfrac{7 \beta +10}{2}\right)^2=16(
2
1α−19
)
2
+(
2
7β+10
)
2
=16
\Rightarrow \boxed{(7\alpha -19)^2+(7\beta +10)^2=64}⇒
(7α−19)
2
+(7β+10)
2
=64
\therefore ∴ The equation of P is of the form
\boxed{(7\alpha -19)^2+(7 \beta +10)^2=64}
(7α−19)
2
+(7β+10)
2
=64
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