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प्रश्न
Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x
उत्तर
Let P (x,3) divides the line segment joining the points
A(-4,2) and B(3,6) in the ratio K:1.
Thus , we have
`(3k-4)/(k+1)=x;` `(6k+2)/(k+1)=3`
for
`6k+2=3(k+1)`
`⇒ 6k+2=3k+3`
`⇒3k=3-2`
`⇒3k=1⇒k=1/3`
∴ Required ratio` 1:3`
a now consider the quation` (3k-4)/(k+1)=x`
Substituting the value of k in the above equation, We have
` (3xx1/3-4)/(1/3+1)= x⇒ -3/(4/3)=x ⇒-9/4=x`
`∴ x=-9/4`
`b.AP=sqrt (((-9)/4+4)^2+(3-2)^2)=sqrt(49/16+1)=sqrt(49+16)/16=sqrt(65/16)`
`⇒ AP=sqrt 65/4 "unit"`
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= `a(1/t^2 + 1) = (a(t^2 + 1))/t^2`
Now `(1)/"SP" + (1)/"SQ" = (1)/(a(t^2 + 1)) + (1 xx t^2)/(a(t^2 + 1)`
= `((1 + t^2))/(a(t^2 + 1)`
`(1)/"SP" + (1)/"SQ" = (1)/a`.
If the line joining the points A(4, - 5) and B(4, 5) is divided by the point P such that `"AP"/"AB" = (2)/(5)`, find the coordinates of P.
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