In how many points the line `y+14=0` cuts the curve whose equation is `x(x^2+x+1)+y=0?`

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

A line 4x + y = 1 passes through the point A (2,-7) meets the line BC whose equation is 3x-4y + 1 =0,at the point B. If AB = AC, find the equation of AC.

Show that the points whose coordinates are (1,4) , (3,-2) and (-3,16) are on the same straight line . Write down the equation of the straight line on which the points lie Verify that this line is perpendicular to the line whose equation is 2x-6y+13=0 .

A line 4x+y=1 passes through the point A(2,-7) and meets line BC at B whose equation is 3x -4y +1=0 , the equation of line AC such that AB=AC is (a) 52x +89y +519=0(b) 52x +89y-519=0 c) 82x +52y+519=0 (d) 89x +52y -519=0

The equation of the line that touches the curves y=x|x| and x^2+(y-2)^2=4 , where x!=0, is: (a)y=4 sqrt(5) x +20 (b)y=4 sqrt(3) x -12 (c)y=0 (d) y=-4 sqrt(5) x -20

The coordinates of a point on the line x + y + 1 = 0 which is at a distance sqrt(2) units from the line 3x + 4y - 2 = 0 are

The equation of a straight line passing through the point (2, 3) and inclined at an angle of tan^(-1)(1/2) with the line y+2x=5 , so the equation of the line is/ are: (a) y=3 (b) x=2 3x+4y-18=0 (d) 4x+3y-17=0

Find the equations of the tangent to the given curves at the indicated points: y=x^(2) at (0,0)

Find the equation of a curve passing through the point (0,0) and whose differential equation is y' = e^(x) sin x .

The distance of the point (3, 5) from the line 2x + 3y - 14 = 0 measured parallel to the line x - 2y = 1 is :