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Standard X

Mathematics

Radical Axis

If a variable...

Question

If a variable line y = 2x + p lies between the circles $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$ and $x^{2} + y^{2} - 16 x - 2 y + 61 = 0$ without intersecting or touching either circles, then number of integral values of p is

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Solution

The correct option is C 7
$C_{1} = (1, 1)$ $C_{2} = (8, 1)$
$r_{1} = 1$
$r_{2} = 2$
let L = 2x – y + P = 0
$L_{11} L_{22}$ < 0 $(1 + p) (15 + p)$ <0 ......(1)
$\frac{| 1 + p |}{\sqrt{5}}$ > 1.....(2)
$\frac{| 15 + p |}{\sqrt{5}}$ >2 .....(3)

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If a variable line y = 2x + p lies between the circles x2+y2−2x−2y+1=0 and x2+y2−16x−2y+61=0 without intersecting or touching either circles, then number of integral values of p is

The correct option is C 7C1=(1,1) C2=(8,1) r1=1 r2=2 let L = 2x – y + P = 0 L11L22 < 0 (1+p)(15+p) <0 ......(1) |1+p|√5 > 1.....(2) |15+p|√5 >2 .....(3)

If a variable line y = 2x + p lies between the circles $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$ and $x^{2} + y^{2} - 16 x - 2 y + 61 = 0$ without intersecting or touching either circles, then number of integral values of p is

The correct option is C 7
$C_{1} = (1, 1)$ $C_{2} = (8, 1)$
$r_{1} = 1$
$r_{2} = 2$
let L = 2x – y + P = 0
$L_{11} L_{22}$ < 0 $(1 + p) (15 + p)$ <0 ......(1)
$\frac{| 1 + p |}{\sqrt{5}}$ > 1.....(2)
$\frac{| 15 + p |}{\sqrt{5}}$ >2 .....(3)