Question
Find the angle between the lines x = a and by + c = 0.
✓
Answer
$\text{x}=\text{a}$
$\Rightarrow\text{m}_1=\frac{1}{0}$
$\text{by}+\text{c}=0$
$\text{y}=\frac{-\text{c}}{\text{b}}$
$\text{m}_2=0$
Comparing with y = mx + c
Then, putting in
$\tan\theta=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$
$=\Bigg|\frac{\frac{1}{0}-0}{1+\frac{1}{0}\times0}\Bigg|$
$=\frac{1}{0}=\infty$
$\Rightarrow\theta=90^\circ$
$\Rightarrow\text{m}_1=\frac{1}{0}$
$\text{by}+\text{c}=0$
$\text{y}=\frac{-\text{c}}{\text{b}}$
$\text{m}_2=0$
Comparing with y = mx + c
Then, putting in
$\tan\theta=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$
$=\Bigg|\frac{\frac{1}{0}-0}{1+\frac{1}{0}\times0}\Bigg|$
$=\frac{1}{0}=\infty$
$\Rightarrow\theta=90^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove that:
$\sin20^\circ\sin40^\circ\sin80^\circ=\frac{\sqrt3}{8}$
→$\sin20^\circ\sin40^\circ\sin80^\circ=\frac{\sqrt3}{8}$
Differentiate in two ways, using product rule and otherwise, the function $(1+2\tan\text{x})(5+4\cos\text{x}).$ verify that the answers are the same.
→A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
Prove the following:
$\cos\Big(\frac{3\pi}{4}+\text{x}\Big)-\cos\Big(\frac{3\pi}{4}-\text{x}\Big)=-\sqrt{2}\sin\text{x}$
→$\cos\Big(\frac{3\pi}{4}+\text{x}\Big)-\cos\Big(\frac{3\pi}{4}-\text{x}\Big)=-\sqrt{2}\sin\text{x}$
$\text {A}$ speaks truth in $75 \%$ of the situations and $\text {B}$ in $80 \%$ of the situations. Find out in how many percent situations do they oppose each other?
→The accompanying Venn diagram shows three events, $A, B,$ and $C,$ and also the probabilities of the various intersections $($for instance, $\text{P}(\text{A}\cap\text{B})=.07)$ Determine:
→
- $\text{P(A)}$
- $\text{P}(\text{B}\cap\bar{\text{C}})$
- $\text{P(A}\cup\text{B})$
- $\text{P(A}\cap\bar{\text{B}})$
- $\text{P(B}\cap\text{C})$
- Probability of exactly one of the three occurs.
Find the equation of the hyperbola, the length of whose latus rectum is $4$ and the eccentricity is $3$.
→Evaluate the following limit:
If $\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{x}^{9}-\text{a}^9}{\text{x}-\text{a}}=\lim\limits_{\text{x}\rightarrow5}(4+\text{x}),$ find all possible value of a.
→If $\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{x}^{9}-\text{a}^9}{\text{x}-\text{a}}=\lim\limits_{\text{x}\rightarrow5}(4+\text{x}),$ find all possible value of a.
If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions:
$\Big(\frac{\text{f}}{\text{g}}\Big)\Big(\frac{1}{2}\Big)$
→$\Big(\frac{\text{f}}{\text{g}}\Big)\Big(\frac{1}{2}\Big)$
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\cos2\text{x}-1}{\cos\text{x}-1}$
→$\lim\limits_{\text{x}\rightarrow0}\frac{\cos2\text{x}-1}{\cos\text{x}-1}$