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Standard XII

Mathematics

Shortest Distance between Two Curves

If the circle...

Question

If the circle $x^{2} + y^{2} = a^{2}$ intersects the hyperbola $x y = c^{2}$ in four points $(x_{i}, y_{i})$ for $i = 1, 2, 3, a n d 4$ then $y_{1} + y_{2} + y_{3} + y_{4} =$

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Solution

The correct option is A
0

Eliminating x

$\Rightarrow y^{4} - a^{2} y^{2} + c^{4} = 0 s u m o f r o o t s : y_{1} + y_{2} + y_{3} + y_{4} = 0$

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Similar questions

If the circle $x^{2} + y^{2} = a^{2}$ intersects the hyperbola $x y = c^{2}$ in four points $(x_{i}, y_{i})$ for $i = 1, 2, 3, a n d 4$ then $y_{1} + y_{2} + y_{3} + y_{4} =$

Q. If the circle

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

intersects the hyperbola xy =

c^{2}

in four points

(x_{i}, y_{i}),

foci = 1, 2, 3 and 4, then

y_{1} + y_{2} + y_{3} + y_{4}

equals

Q. If the circle

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

intersects the hyperbola

x y = c^{2}

at four points

P (x_{1}, y_{1}), Q (x_{2}, y_{2}), R (x_{3}, y_{3}), a n d S (x_{4}, y_{4})

, then

Q. If the circle

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

intersect the hyperbola

x y = c^{2}

in four points P

(x_{1}, y_{2}), Q (x_{2}, y_{2}), R (x_{3}, y_{3}), S (x_{4}, y_{4}),

then which of the following does not hold

Q. If the circle

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

intersects the hyperbola

x y = c^{2}

in four points

P (x_{1}, y_{1}), Q (x_{2}, y_{2}), R (x_{3}, y_{3}), S (x_{4}, y_{4})

, then -

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If the circle x2+y2=a2 intersects the hyperbola xy=c2 in four points (xi,yi) for i=1,2,3, and 4 then y1+y2+y3+y4=

The correct option is A 0 Eliminating x ⇒y4−a2y2+c4=0sum of roots :y1+y2+y3+y4=0

If the circle $x^{2} + y^{2} = a^{2}$ intersects the hyperbola $x y = c^{2}$ in four points $(x_{i}, y_{i})$ for $i = 1, 2, 3, a n d 4$ then $y_{1} + y_{2} + y_{3} + y_{4} =$

The correct option is A
0

Eliminating x

$\Rightarrow y^{4} - a^{2} y^{2} + c^{4} = 0 s u m o f r o o t s : y_{1} + y_{2} + y_{3} + y_{4} = 0$