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The foci of the hyperbola 2x2 − 3y2 = 5 are
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The equation of the hyperbola whose centre is (6, 2) one focus is (4, 2) and of eccentricity 2 is
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Find the axes, eccentricity, latus-rectum and the coordinates of the foci of the hyperbola 25x2 − 36y2 = 225.
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Find the equation of the hyperbola satisfying the given condition :
foci (± \[3\sqrt{5}\] 0), the latus-rectum = 8
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find the equation of the hyperbola satisfying the given condition:
foci (± \[3\sqrt{5}\] 0), the latus-rectum = 8
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find the equation of the hyperbola satisfying the given condition:
foci (0, ± 12), latus-rectum = 36
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Write the eccentricity of the hyperbola whose latus-rectum is half of its transverse axis.
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Write the length of the latus-rectum of the hyperbola 16x2 − 9y2 = 144.
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If the latus-rectum through one focus of a hyperbola subtends a right angle at the farther vertex, then write the eccentricity of the hyperbola.
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The latus-rectum of the hyperbola 16x2 − 9y2 = 144 is
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Find the equations of the circles which pass through the origin and cut off equal chords of \[\sqrt{2}\] units from the lines y = x and y = − x.
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Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.
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Write the coordinates of the centre of the circle passing through (0, 0), (4, 0) and (0, −6).
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If the abscissae and ordinates of two points P and Q are roots of the equations x2 + 2ax − b2 = 0 and x2 + 2px − q2 = 0 respectively, then write the equation of the circle with PQ as diameter.
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Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.
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If the radius of the circle x2 + y2 + ax + (1 − a) y + 5 = 0 does not exceed 5, write the number of integral values a.
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Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).
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If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are
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If 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius is
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The equation x2 + y2 + 2x − 4y + 5 = 0 represents
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