(B) Two points $(x_1, y_1)$ and $(x_2, y_2)$ are conjugate with respect to the circle $x^2+y^2=r^2$ if $x_1x_2 + y_1y_2 = r^2$.Given the points $(1, a

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(B) Two points $(x_1, y_1)$ and $(x_2, y_2)$ are conjugate with respect to the circle $x^2+y^2=r^2$ if $x_1x_2 + y_1y_2 = r^2$.Given the points $(1, a)$ and $(b, 2)$ and the circle $x^2+y^2=25$,we have $r^2=25$.Substituting the coordinates into the condition,we get $(1)(b) + (a)(2) = 25$.This simplifies to $b + 2a = 25$.We need to find the value of $4a + 2b$.Multiplying the equation $2a + b = 25$ by $2$,we get $2(2a + b) = 2(25)$,which is $4a + 2b = 50$.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

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If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b=$

AP EAMCET 2020 All AP EAMCET

A
$25$
B
$50$
C
$75$
D
$100$

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

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