QJEEM22Ma333e: JEE Main 2022 Mathematics - Class 11 JEEM22Ma333e Solution: If the circle x 2 + y 2 − 2 g x + 6 y − 19 c = 0 , g , c ∈ R…

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QJEEM22Ma333e: JEE Main 2022 Mathematics - Class 11 JEEM22Ma333e Solution: If the circle x 2 + y 2 − 2 g x + 6 y − 19 c = 0 , g , c ∈ R…

If the circle $x^{2} + y^{2} - 2 g x + 6 y - 19 c = 0, g, c \in R$ passes through the point $(6, 1)$ and its centre lies on the line $x - 2 c y = 8$ , then the length of intercept made by the circle on $x$ -axis is :

Multiple Choice Options

A 11
B 4
C 3
D 223

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Accepted Answer

Circle : $x^{2} + y^{2} - 2 g x + 6 y - 19 c = 0$

It passes through $h (6, 1)$

$\Rightarrow 36 + 1 - 12 g + 6 - 19 c = 0$

$= 12 g + 19 c = 43$ ..... (1)

Line $x - 2 c y = 8$ passes through centre

$\Rightarrow g + 6 c = 8$ ...... (2)

From (1) & (2)

$g = 2, c = 1$

$C : x^{2} + y^{2} - 4 x + 6 y - 19 = 0$

x intercept $= 2 \sqrt{g^{2} - C}$

$= 2 \sqrt{4 + 19}$

$= 2 \sqrt{23}$

QJEEM22Ma333e: JEE Main 2022 Mathematics - Class 11 JEEM22Ma333e Solution: If the circle x 2 + y 2 − 2 g x + 6 y − 19 c = 0 , g , c ∈ R…

Multiple Choice Options

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