Angle between pair of straight lines

Q.

Tangent of acute angle between pair of straight lines $a{x}^2+2hxy+b{y}^2$ is given by $tan\theta =\left|\frac{2\sqrt{h^2-ab}}{a-b}\right|$

1. False

2. True

Q.

The angle between the pair of straight lines $x^2+4y^2-7xy=0,$ is

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2. 

3. 

4. 

Q. The angle between the lines joining the origin to the points of intersection of the line y = 3x + 2with the curve $x^2$ + 2xy + ${3y}^2$ + 4x + 8y = 11, is

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4. 

Q.

Two equal sides of an isosceles triangle are given by the equations $7x-y+3=0$ and $x+y-3=0$ and its third side passes through the point (1, 10), Determine the equation of the third side.

Q.

Find the acute angle (in degree) between the pair of straight lines $4x^2+14xy+6y^2=0$

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Q. Suppose $f\left(x\right)=$ $\{\begin{array}{cc}a+bx,& x<1\\ 4,& x=1\\ b-ax& x>1\end{array}$ and if $\underset{x\to 1}{lim}f\left(x\right)=f\left(1\right)$, then what is the possible value of $a,b$?

Q.

tangent of Acute angle between pair of straight lines $a{x}^2+2hxy+b{y}^2$ is given by $tan\theta =\left|\frac{2\sqrt{h^2-ab}}{a-b}\right|$

1. True

2. False

Q. Solve the following pair of linear equations graphically. $x+3y=6;2x-3y=12$. Also find the area of the triangle formed by the lines representing the given equations with $y-$axis.

Q. Find the equation for the ellipse that satisfies the given condition:

Q. In the triangle $ABC$ with vertices $A(2,3),B(4,-1)$ and $C(1,2)$, find the equation and length of altitude from the vertex $A$.

Q. The equation of the line which passes through the point $(3,4)$ and the sum of its intercept on the axes is $14$ is :

1. $4x-3y=24,x-y=7$
2. $4x+3y=24,x+y=7$
3. $4x+3y+24=0,x+y+7=0$
4. $4x-3y+24=0,x-y+7=0$

Q.

Find the acute angle (in degree) between the pair of straight lines $4x^2+14xy+6y^2=0$

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Q. Find the value of $p$ so that the three lines $3x+y-2=0,px+2y-3=0$ and $2x-y-3=0$ may intersect at one point.