Angle between Pair of Straight Lines

Q. The minimum dis†an ce between the parabolas y^2 – 4x –8y + 40 = 0 and x^{2 }– 8x – 4y + 40 = 0 is

Q.

Find the number of solutions for $\left[x\right]=\left\{x\right\}$. Where $\left[x\right],\left\{x\right\}$ represents greatest integer and fractional part of x.

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Q.

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

1. $ta{n}^{-1}\frac{1}{3}$

2. $ta{n}^{-1}3$

3. $ta{n}^{-1}\frac{\sqrt{33}}{5}$

4. $ta{n}^{-1}\frac{5}{\sqrt{33}}$

Q. A rod of length $12$ cm moves with it ends always touching the coordinate axes. Dertermine the equation of the locus of a point $P$ on the rod which is $3$ cm from the end in contact with the $x$-axis

Q. In $∆ABC,\frac{b+c}{12}=\frac{c+a}{13}=\frac{a+b}{15}$. Prove that $\frac{\cos A}{2}=\frac{\cos B}{7}=\frac{\cos C}{11}$.

Q. Find the angle between the $x$-axis and the line joining the points $(3,-1)$ and $(4,-2)$.

Q.

If the acute angles between the pairs of lines $3x^2-7xy+4y^2=0$ and $6x^2-5xy+y^2=0$ be ${\theta }_1$ and ${\theta }_2$ respectively, then

1. 

2. 

3. 

4. None of these

Q.

If the acute angles between the pairs of lines $3x^2-7xy+4y^2=0$ and $6x^2-5xy+y^2=0$ be ${\theta }_1$ and ${\theta }_2$ respectively, then

1. ${\theta }_1$ = ${\theta }_2$

2. ${\theta }_1$ = 2${\theta }_2$

3. $2{\theta }_1$ = ${\theta }_2$

4. ${\theta }_1$ = 5${\theta }_2$