JEE MATHEMATICS MCQ: CIRCLES

1 Medium

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Application +4 | -1

\frac{x}{\alpha } + \frac{y}{\beta } = 1

touches the circle

{x^2} + {y^2} = {a^2}

, the point

\left( {1/\alpha ,1/\beta } \right)

lies on a/an

View answer and explanation

Correct option: B

Circle

Option B (Circle) is correct because the locus of the point (1/α, 1/β) is a circle, derived from the condition of tangency to the given circle.

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{\left( {{\alpha ^2}{x^2} - 2\alpha \mathrm{ }x + 1} \right)^{51}},

x

\left( {\alpha ,2{\alpha ^2}} \right)

{x^2} + {y^2} = 4,

{x^2} + {y^2} - 2x + 4y - 4 = 0

{x^2} + {y^2} = {a^2}

\left( {{x_1},{y_1}} \right)

\quad \alpha, \beta

\gamma

P, Q

x^2+y^2=1

A

(-1,0)

A P, A Q

A R

G P

\cos \alpha / 2, \cos \beta / 2

\cos \gamma / 2

x+y=6

x+2 y=4

x+y=5

x-y=1

9 \pi