Find the slope of a common tangent to the ellipse a2x2+b2y2=1 and a concentric circle of radius r˙
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(acosθ1,asinθ1),B(acosθ2asinθ2),andC(acosθ3,asinθ3) is equilateral, then prove that cosθ1+cosθ2+cosθ3=sinθ1+sinθ2+sinθ3=0.
What does the equation 2x2+4xy−5y2+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 450 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.