How many real tangents can be drawn from the point (4, 3) to the hyperbola 16x2−9y2=1?
Find the equation of these tangents and the angle between them.
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Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x+y=16.
The focus of a parabolic mirror as shown in is at a distance of 5 cm from its vertex. If the mirror is 45 cm deep, find the distance AB
Find the centre and the radius of the circle x2+y2+8x+10y−8=0.
Find the equations of the hyperbola satisfying the given conditions :Foci (0,±10), passing through (2,3)
Find the equation of the ellipse whose vertices are (±13,0)and foci are (±5,0).
XYand XprimeYprimeare two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XYat A and XprimeYprimeat B. Prove that ∠AOB = 90o
is a variable point on the lines ∣x∣
=6. IF AB≤4
, then find the number of position of B
with integral coordinates.
A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.