Intercept Form of a Line

Q. Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Q. Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Q.

Angles made by the lines represented by the equation xy + y = 0 with y-axis are

1. 

2. 

3. 

4. 

Q.

Solve the following system of linear equation graphically:

$2x+3y=12;x-y=1$.Shade the area bounded by these two lines and the x-axis.

Q.

In a $△$ ABC, the tangent of half the difference of two angles is one - third the tangent of half the sum of the two angles. The ratio of the sides opposite the angles is

1. 2:3

2. 1:3

3. 2:1

4. 3:4

Q.

Find the equation of a straight line which passes through the point (3, 4) and sum of its intercepts on the x and y axis is 14.

1. x + y = 7

2. 4x + 3y = 24

3. x + y = 14

4. 3x + 4y = 24

Q.

Reduce the following equations into intercept form and find their intercepts on the axis.

(i) 3x + 2y - 1 2 = 0, (ii) 4x- 3y = 6, (iii) 3y + 2 = 0

Q. Reduce the following equations into intercept form and find their intercepts on the axes. (i) 3 x + 2 y – 12 = 0 (ii) 4 x – 3 y = 6 (iii) 3 y + 2 = 0.

Q.

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that $\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}$

Q. Find the equation of the line passing through the point of intersection of the lines 4 x + 7 y – 3 = 0 and 2 x – 3 y + 1 = 0 that has equal intercepts on the axes.

Q. Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively.

Q.

Find the distance between $P(x_1,y_1)$ and $Q(x_2,y_2)$ when: (i) PQ is parallel to the y-axis (ii) PQ is parallel to the x-axis.

Q.

Solve the following system of linear equations graphically, Also find the points where the lines meet the x−axis or y−axis.

$\left(ix\right)2x-5y+4=0;2x+y-8=0,y-axis$

Q. The locus of the midpoint of the portion between the axes of
$xcos\alpha +ysin\alpha =p,$ where p is a constant, is

1. $x^2+y^2=\frac{4}{p^2}$
2. $x^2+y^2=4p^2$
3. $\frac{1}{x^2}\frac{1}{y^2}=\frac{2}{p^2}$
4. $\frac{1}{x^2}+\frac{1}{y^2}=\frac{4}{p^2}$

Q. Reduce the following equations into slope-intercept form and find their slopes and the y -intercepts. (i) x + 7 y = 0 (ii) 6 x + 3 y – 5 = 0 (iii) y = 0

Q.

The locus of the midpoint of the portion between the axes of
$xcos\alpha +ysin\alpha =p,$ where p is a constant, is

1. $\frac{1}{x^2}\frac{1}{y^2}=\frac{2}{p^2}$

2. $\frac{1}{x^2}+\frac{1}{y^2}=\frac{4}{p^2}$

3. $x^2+y^2=\frac{4}{p^2}$

4. $x^2+y^2=4p^2$

Q. The equation(s) of the line(s) which cut-off intercepts on the axes whose sum and product are 1 and -6 respectively, is/are

1. 2x-3y-6 = 0
2. 2x-3y = -6
3. -3x+2y = 6
4. 3x - 2y = 6

Q. The equation of the line whose X and Y intercepts are respectively twice and thrice of those by the line 2x+5y = 10, will be .

1. 5x+3y = 30
2. 3x+5y = 30
3. 15x+4y = 60
4. 4x+15y = 60

Q.

Draw the graph of the following equations. Also Determine the Coordinates of the vertices of the triangle formed by these lines and the x-axis.

$4x-y-8=0;2x-3y+6=0$

Q. The sum of the intercepts made by a line on the co-ordinate axes is 2. If it passes through (4, -3), find its equation.

Q. 6. 2x + y = 7 is one of the bisectors of the angles between the lines represented by α(x – 2)² + 2γ(x – 2) (y – 3) + β(y – 3)² = 0. Then the intercepts made by the other bisector on the x-axis and y-axis respectively.
(a) –4, 2 (b) 4, –2 (c) 2, –4 (d) –2, 4

7. If A(1, 2) and B(4, 3) are two points, then a point P on the line 3x – 4y + 7 = 0 such that |AP – PB| is maximum, is
(a) $\left(\frac{8}{5},\frac{1}{5}\right)$ (b) $\left(-\frac{1}{5},\frac{8}{5}\right)$ (c) $\left(\frac{8}{5},-\frac{1}{5}\right)$ (d) $\left(\frac{1}{5},\frac{3}{5}\right)$

Q. find the equation of a line perpendicular to the line x- 2y +3 = 0 and passing through the points (1, -2)

Q. If h denote the A.M, k denote G.M of the intercepts made on axes by the lines passing through (1, 1) then (h, k) lies on

1. $y^2=2x$
2. $y^2=4x$
3. $y=2x$
4. $x+y=2xy$

Q. A vertex of an equilateral triangle is (2, 3) and the opposite side is x + y = 2. Find the equations of the other sides.

Q. The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p and q are the intercepts of the line L on the new axes, then $\frac{1}{a^2}-\frac{1}{p^2}+\frac{1}{b^2}-\frac{1}{q^2}$ is equal to

1. 0
2. 1
3. -1
4. none of these