Distinguish Acute Angle Bisectors and Obtuse Angle Bisectors

Q.

If the lines $y=3x+1$ and $2y=x+3$ are equally inclined to the line $y=mx+4$, find the value of m.

Q. The obtuse angle between the lines y = -2 and y = x +2 is __ (degree)

Q.

If $L_1$ and $L_2$ be the angle bisectors of two lines, then the angle between $L_1$ and $L_2$ is${90}^{\circ }$ .

1. False

2. True

Q.

If A+B =${225}^{\circ }$, (1+cotA)(1+cotB) equal to

1. cotAcotB

2. 2 (cotA+cotB)

3. 2cotAcotB

4. cotA+cotB

Q. Through the vertex O of the parabola $y^2=4ax$ two chords OP & OQ are drawn and the circles on OP &OQ as diameter intersect in R. If ${\theta }_1$, ${\theta }_2$ & $\varphi$ are the inclinations of the tangents at P & Q on the parabola and the line through O, R respectively, then the value of $cot{\theta }_1+cot{\theta }_2$ is

1. 
2. 
3. 
4. 

Q.

The lines $(lx+my{)}^2-3(mx-ly{)}^2=0$ and lx + my + n = 0 form

1. None of these

2. An equilateral triangle

3. An isosceles triangle

4. A right angled triangle

Q. The obtuse angle between the lines $x-\sqrt{3}y=5$ and $\sqrt{3}x-y=7$ is

1. ${105}^{\circ }$
2. ${150}^{\circ }$
3. ${120}^{\circ }$

Q. The number of real values of λ for which the lines x − 2y + 3 = 0, λx + 3y + 1 = 0 and 4x − λy + 2 = 0 are concurrent is
(a) 0
(b) 1
(c) 2
(d) Infinite

Q. The obtuse angle between the lines y = -2 and y = x +2 is __ (degree)

Q. Find value of $(a^2+\sqrt{a^2-1}{)}^4+(a^2-\sqrt{a^2-1}{)}^4$ if a=$\sqrt{5}$.

Q.

What are the coordinates of a point on the hyperbola $16x^2-{25}^2=1$ given by the parameter ${30}^{\circ }$?

1. \)

2. \)

3. \)

4. \)

Q. Write the equation of the directrix of the parabola x² − 4x − 8y + 12 = 0.

Q.

Acute angle between the lines represented by $(x^2+y^2)\sqrt{3}=4xy$ is

1. 

2. 

3. 

4. None of these

Q.

how many integral solutions are possible for the equation n * y = 100 if n and y are natural numbers?

Q. The obtuse angle between the lines y = -2 and y = x +2 is __ (degree)

Q. The equation of the line bisecting the obtuse angle between y - x = 2 and √3 y + x = 5 is

Q. (4) x y2-2x - 2y - 470A circle has radius 3 units and its centre lies on the line y= x-1. If it passes through (7, 3), then its equations7.(1) x2y8x + 10y3= 0(2) x212 10x