# Point Slope Form of a Line

## Trending Questions

**Q.**

Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).

**Q.**Find the equation of the line which passes through the point (–4, 3) with slope .

**Q.**

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

**Q.**

If y = 2x is a chord of the circle x2+y2−10x=0, find the equation of a circle with this chord as diameter.

Or

Find the equation of ellipse whose foci are (2, 3) and (- 2, 3) and whose semi-minor axis is √5

**Q.**The equation of the line passing through (3, 1) parallel to the line y=2x+3 is

- y = 2x - 5
- x + 2y = 5
- y = 2x + 1

**Q.**

Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts.

(i) x + 7y = 0, (ii) 6x + 3y -5 = 0, (iii) y = 0

**Q.**

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

**Q.**

Equation of the straight line passing through the point of intersection of the lines 3x+4y=7, x−y+2=0 and having slope 3 is

21x−7y+16=0

21x−7y+12=0

9x−3y+14=0

9x−3y+5=0

**Q.**

A person standing at the junction (crossing) of two straight paths represented by the equations 2x−3y+4=0 and 3x+4y−5=0 wants to reach the path whose equation is 6x−7y+8=0 in the least time. Find equation of the path that he should follow.

**Q.**Solve the following systems of linear inequations graphically:

(i) 2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0

(ii) 2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0

(iii) x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0

(iv) x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0

(v) 2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

**Q.**

A line through the point A(2, 0), which makes an angle of 30∘ with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15∘. The equation of the straight line in the new position is

**Q.**3. Locus of the middle point of the intercept on the line y=x+c made by the lines 2x+3y=5 and 2x+3y=8, c being a parameter, is

**Q.**Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is

(a) $\frac{35}{\sqrt{34}}$

(b) $\frac{1}{3\sqrt{34}}$

(c) $\frac{35}{3\sqrt{34}}$

(d) $\frac{35}{2\sqrt{34}}$

(e) 35

**Q.**The equation of the parabola whose focus is (1, −1) and the directrix is x + y + 7 = 0 is

(a) x

^{2}+ y

^{2}− 2xy − 18x − 10y = 0

(b) x

^{2}− 18x − 10y − 45 = 0

(c) x

^{2}+ y

^{2}− 18x − 10y − 45 = 0

(d) x

^{2}+ y

^{2}− 2xy − 18x − 10y − 45 = 0

**Q.**The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is

(a) 5x + 3y − 20 = 0

(b) 3x − 5y + 7 = 0

(c) 3x − 5y + 6 = 0

(d) 5x + 3y + 7 = 0

**Q.**A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is

(a) $\frac{1}{3}$

(b) 2/3

(c) 1

(d) 4/3

**Q.**The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x

^{2}− y

^{2}−2x + 4y − 3 = 0, is

(a) x

^{2}+ y

^{2}− 2x − 4y + 4 = 0

(b) x

^{2}+ y

^{2}+ 2x + 4y − 4 = 0

(c) x

^{2}+ y

^{2}− 2x + 4y + 4 = 0

(d) none of these

**Q.**Find the equation of the line passing through the point (−3, 5) and perpendicular to the line joining (2, 5) and (−3, 6).

**Q.**Find the equation of the line whose perpendicular distance from the origin is 5 units and angle made by the perpendicular with positive X-axis is 30 degree

**Q.**Find the equation of the line which passes though and is inclined with the x -axis at an angle of 75°.

**Q.**The equation of the parabola whose vertex is (a, 0) and the directrix has the equation x + y = 3a, is

(a) x

^{2}+ y

^{2}+ 2xy + 6ax + 10ay + 7a

^{2}= 0

(b) x

^{2}− 2xy + y

^{2}+ 6ax + 10ay − 7a

^{2}= 0

(c) x

^{2}− 2xy + y

^{2}− 6ax + 10ay − 7a

^{2}= 0

(d) none of these

**Q.**43.equation of circle touching the lines |x-2|+|y-3|=4

**Q.**Find the equation of the line perpendicular to x-axis and having intercept − 2 on x-axis.

**Q.**L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero. The line L will always pass through

(a) (1, 1)

(b) (2, 1)

(c) (1, 2)

(d) none of these

**Q.**The equation of the line perpendicular to y=3x+5, passing through the point (-1, -2) is

- x+3y+7=0
- y=3x+1
- 2x+3y+8=0

**Q.**Show that the area of the triangle formed by the lines y = m

_{1}x, y = m

_{2}x and y = c is equal to $\frac{{c}^{2}}{4}\left(\sqrt{33}+\sqrt{11}\right),$ where m

_{1}, m

_{2}are the roots of the equation ${x}^{2}+\left(\sqrt{3}+2\right)x+\sqrt{3}-1=0.$

**Q.**Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x-axis such that sin α = $\frac{1}{3}$.

**Q.**The straight line x+2y=1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

- 4√5
- √54
- 2√5
- √52

**Q.**A variable line L is drawn through O(0, 0) to meet L1:x−y−8=0 and L2:x−y−16=0 at points A and B respectively. A point P is taken on L such that 14 OP=1OA+1OB. Then the locus of P is

- 3x−3y=4
- 3x+3y−4=0
- 3x−3y=16
- x=y

**Q.**If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.