Equations of two diameters of a circle are 2 x - 3 y = 5 and 3 x - 4 y = 7 . The line joining the points ( - 22 7 , - 4 ) and ( - 1 7 , 3 ) intersect the circle at only one point P then 29 6 is equal to

Question

Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersect the circle at only one point $P (α, β)$ then $\frac{29}{6} (β - α)$ is equal to ______

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(7)

$Equation of A B is 7 X - 3 Y + 10 = 0$ $(- \frac{22}{7}, - 4)$

$Equation of C P is 3 x + 7 y - 4 = 0$ $\dots \dots (i i)$

$α = - \frac{41}{29}$ $β = \frac{1}{29}$

Solution

Q.
Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersect the circle at only one point $P (α, β)$ then $\frac{29}{6} (β - α)$ is equal to ______

Ans.
(7)

$Equation of A B is 7 X - 3 Y + 10 = 0$ $\dots \dots (I)$

$Equation of C P is 3 x + 7 y - 4 = 0$ $\dots \dots (i i)$

$α = - \frac{41}{29}$ $β = \frac{1}{29}$

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Solution

Q. Equations of two diameters of a circle are 2x-3y=5 and 3x-4y=7. The line joining the points (-227,-4) and (-17,3) intersect the circle at only one point P(α,β) then 296(β-α) is equal to ______

Ans. (7) Equation of AB is 7X-3Y+10=0 ……(I) Equation of CP is 3x+7y-4=0 ……(ii) α=-4129 β=129

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Q.
Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersect the circle at only one point $P (α, β)$ then $\frac{29}{6} (β - α)$ is equal to ______

Ans.
(7)

$Equation of A B is 7 X - 3 Y + 10 = 0$ $\dots \dots (I)$

$Equation of C P is 3 x + 7 y - 4 = 0$ $\dots \dots (i i)$

$α = - \frac{41}{29}$ $β = \frac{1}{29}$