(2)

Locus of all such points from where the tangents drawn to the ellipse x^2/a^2 + y^2/b^2 = 1 are always inclined at 45^0 is: (A) (x^2 + y^2 - a^2 - b^2)^2 = (b^2 x^2 + a^2 y^2 - 1) (B) (x^2 + y^2 - a^2 - b^2)^2 = 4(b^2 x^2 + a^2 y^2 - 1) (C) (x^2 + y^2 - a^2 - b^2)^2 = 4(a^2 x^2 + b^2 y^2 - 1) (D) none of these

The locus of a point, from where the tangents to the rectangular hyperbola x^2-y^2=a^2 contain an angle of 45^0 , is (a) (x^2+y^2)^2+a^2(x^2-y^2)=4a^2 (b) 2(x^2+y^2)^2+4a^2(x^2-y^(2))=4a^2 (c) (x^2+y^2)^2+4a^2(x^2-y^2)=4a^2 (d) (x^2+y^2)+a^2(x^2-y^(2))=a^4

The locus of a point, from where the tangents to the rectangular hyperbola x^2-y^2=a^2 contain an angle of 45^0 , is (a) (x^2+y^2)^2+a^2(x^2-y^2)=4a^2 (b) 2(x^2+y^2)^2+4a^2(x^2-y^(2))=4a^2 (c) (x^2+y^2)^2+4a^2(x^2-y^2)=4a^2 (d) (x^2+y^2)+a^2(x^2-y^(2))=a^4

If a circle passes through the point (a, b) and cuts the circle x^2 + y^2 = 4 orthogonally, then the locus of its centre is (a) 2ax+2by-(a^(2)+b^(2)+4)=0 (b) 2ax+2by-(a^(2)-b^(2)+k^(2))=0 (c) x^(2)+y^(2)-3ax-4by+(a^(2)+b^(2)-k^(2))=0 (d) x^(2)+y^(2)-2ax-3by+(a^(2)-b^(2)-k^(2))=0