Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the point on the hyperbola $x_{2}−9y_{2}=9$ where the line $5x+12y=9$ touches it.

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If from any point $P$ on the circle $x_{2}+y_{2}+2gx+2fy+c=0,$ tangents are drawn to the circle $x_{2}+y_{2}+2gx+2fy+csin_{2}α+(g_{2}+f_{2})cos_{2}α=0$ , then find the angle between the tangents.

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle $x_{2}+y_{2}=9$ and the line joining their points of contact.

Find the length of the tangent drawn from any point on the circle $x_{2}+y_{2}+2gx+2fy+c_{1}=0$ to the circle $x_{2}+y_{2}+2gx+2fy+c_{2}=0$

Find the equation of the circle with radius 5 whose center lies on the x-axis and passes through the point (2, 3).

Find the length of intercept, the circle $x_{2}+y_{2}+10x−6y+9=0$ makes on the x-axis.

Find the equation of the circle passing through the origin and cutting intercepts of lengths 3 units and 4 unitss from the positive exes.

Two circles with radii $aandb$ touch each other externally such that $θ$ is the angle between the direct common tangents, $(a>b≥2)$ . Then prove that $θ=2sin_{−1}(a+ba−b )$ .

Statement 1 : The equation of chord through the point $(−2,4)$ which is farthest from the center of the circle $x_{2}+y_{2}−6x+10y−9=0$ is $x+y−2=0$ . Statement 1 : In notations, the equation of such chord of the circle $S=0$ bisected at $(x_{1},y_{1})$ must be $T=S˙$