Mathematics - Circle Question with Solution | TestHub

MathematicsCircleChord, Intercept (Made by the circle)Medium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q90-92: The line x+2y+a=0 meets x²+y²=4 at distinct points A and B. The line 12x-6y-41=0 meets x²+y²-4x-2y+1=0 at distinct points C and D.

$x + 2 y + a = 0$ intersects $x^{2} + y^{2} = 4$ at distinct points $A, B$ . The line $12 x - 6 y - 41 = 0$ intersects $x^{2} + y^{2} - 4 x - 2 y + 1 = 0$ at distinct points $C, D$ . How many integer values of $a$ satisfy the two-intersection condition?

Options:

Answer:

Solution:

The line $x + 2 y + a = 0$ is at distance $∣ a ∣/ 5$ from the origin; two distinct intersections with the radius- 2 circle require $a^{2} < 20$ . The nine integers are -4 through 4 .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Chord, Intercept (Made by the circle)

⏱ 2mℹ️ Source: QB

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