Class 11

Math

Co-ordinate Geometry

Conic Sections

the eccentricity of the locus of the locus of point (3h+2,k), where (h,k) lies on the ellipse $x_{2}+y_{2}=1$, is

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Find the equation of the small circle that touches the circle $x_{2}+y_{2}=1$ and passes through the point $(4,3)˙$

The circle $x_{2}+y_{2}−4x−4y+4=0$ is inscribed in a variable triangle $OAB˙$ Sides $OA$ and $OB$ lie along the x- and y-axis, respectively, where $O$ is the origin. Find the locus of the midpoint of side $AB˙$

Two fixed circles with radii $r_{1}andr_{2},(r_{1}>r_{2})$ , respectively, touch each other externally. Then identify the locus of the point of intersection of their direction common tangents.

Let A (-2,2)and B (2,-2) be two points AB subtends an angle of $45_{∘}$ at any points P in the plane in such a way that area of $ΔPAB$ is 8 square unit, then number of possibe position(s) of P is

If the two circles $2x_{2}+2y_{2}−3x+6y+k=0$ and $x_{2}+y_{2}−4x+10y+16=0$ cut orthogonally, then find the value of $k$ .

The tangent to the circle $x_{2}+y_{2}=5$ at $(1,−2)$ also touches the circle $x_{2}+y_{2}−8x+6y+20=0$ . Find the coordinats of the corresponding point of contact.

The lengths of the tangents from $P(1,−1)$ and $Q(3,3)$ to a circle are $2 $ and $6 $ , respectively. Then, find the length of the tangent from $R(−1,−5)$ to the same circle.

Find the equation of the circle which passes through (1, 0) and (0, 1) and has its radius as small as possible.