PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

4x² + y = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas 

y² − 4y − 3x + 1 = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y² − 4y + 4x = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola 

 y² + 4x + 4y − 3 = 0 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y² = 8x + 8y 

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y² = 8x + 8y

Find the equation of the line parallel to x-axis and having intercept − 2 on y-axis.

Draw the lines x = − 3, x = 2, y = − 2, y = 3 and write the coordinates of the vertices of the square so formed.

Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.

Find the equation of the straight line passing through (−2, 3) and inclined at an angle of 45° with the x-axis.

Find the equation of the line passing through (0, 0) with slope m.

Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.

Find the equation of the straight line which passes through the point (1,2) and makes such an angle with the positive direction of x-axis whose sine is \[\frac{3}{5}\].

Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.

Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.

Prove that the perpendicular drawn from the point (4, 1) on the join of (2, −1) and (6, 5) divides it in the ratio 5 : 8.