Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the slope of a common tangent to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ and a concentric circle of radius $r˙$

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Find the equation of the parabola that satisfies the given conditions:Focus $(0,3)$; directrix $y=3$

In what ratio does the x=axis divide the line segment joining the points $(2,−3)$ and (5, 6)?

If the points $(1,1):(0,sec_{2}θ);$ and $(cosec_{2}θ,0)$ are collinear, then find the value of $θ$

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.

If $ABC$ having vertices $A(acosθ_{1},asinθ_{1}),B(acosθ_{2}asinθ_{2}),andC(acosθ_{3},asinθ_{3})$ is equilateral, then prove that $cosθ_{1}+cosθ_{2}+cosθ_{3}=sinθ_{1}+sinθ_{2}+sinθ_{3}=0.$

What does the equation $2x_{2}+4xy−5y_{2}+20x−22y−14=0$ become when referred to the rectangular axes through the point $(−2,−3)$ , the new axes being inclined at an angle at $45_{0}$ with the old axes?

Fill in the blanks:(i) The centre of a circle lies in of the circle. (exterior/ interior)(ii) A point, whose distance from the centre of a circle is greater than its radius lies inof the circle. (exterior/ interior)(iii) The longest chord of a circle is a_________ of the circle.(iv) An arc is a _________when its ends are the ends of a diameter.(v) Segment of a circle is the region between an arc and________ of the circle.(vi) A circle divides the plane, on which it lies, in________ parts.

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.