Mathematics Tes...

Find the equation of the line passing through the intersection of the lines x + 2y - 3 = 0 and 4x – y + 7 = 0 and which is parallel to y – x + 10 = 0.

A line which is parallel to the x-axis and crosses the curve y =√x at an angle of 45^o is

The locus of the point of intersection of the lines x sin θ + (1 – cos θ) y = a sin θ and x sin  – (1 + cos θ ) y + a sin θ = 0 is

The equation of a circle touching the coordinate axes and the line x cos α + y sin α = 2 is x² + y² – 2gx + 2gy + g² = 0, where g is equal to

C₁ and C₂ are circles of unit radii with centres at (0, 0) and (1, 0), respectively. C₃ is a circle of unit radius, which passes through the centres of the circles C₁ and C₂ and has its centre above the x-axis. The equation of the common tangent to C₁ and C₃, which does not pass through C₂, is

A chord of the circle x² + y² – 4x – 6y = 0 passing through the origin subtends an angle tan^–1(7/4) at the point where the circle meets the positive y-axis. The equation of the chord is

If a circle passes through (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is

The circles x² + y² – 10x + 16 = 0 and x² + y² = r² intersect each other at two distinct points if

Let f(x) = sin x + cos x. Then,