From the point A(4,3), tangent are drawn to the ellipse 16x2+9y2=1 to touch the ellipse at B and CE˙F is a tangent to the ellipse parallel to line BC and towards point A˙ Then find the distance of A from EF˙
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If the circle x2+y2=1
is completely contained in the circle x2+y2+4x+3y+k=0
, then find the values of k˙
Find the equation of the circle which passes through the points (3,−2)and(−2,0)
and the center lies on the line 2x−y=3
be a point on the circle x2+y2=9,Q
a point on the line 7x+y+3=0
, and the perpendicular bisector of PQ
be the line x−y+1=0
. Then the coordinates of P
Find the equation of the normals to the circle x2+y2−8x−2y+12=0
at the point whose ordinate is −1
Find the point of intersection of the circle x2+y2−3x−4y+2=0
with the x-axis.
is the variable point on the circle with center at CC˙A
are perpendiculars from C
on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle PAB
is a circle with center at the centroid of triangle CAB
and radius equal to the one-third of the radius of the given circle.
Find the equation of the circle which cuts the three circles x2+y2−3x−6y+14=0,x2+y2−x−4y+8=0,
Find the area of the triangle formed by the tangents from the point (4,
3) to the circle x2+y2=9
and the line joining their points of contact.