AP EAMCET · Maths · Straight Lines
If a straight line through the point \(P(1,2)\), which makes an angle \(45^{\circ}\) with the \(X\)-axis, meets the line \(3 x+4 y+5=0\) at \(Q\), then length of \(P Q\) equals ......... units
- A \(\frac{16 \sqrt{2}}{7}\)
- B \(\frac{\sqrt{7}}{2}\)
- C \(\frac{7 \sqrt{2}}{16}\)
- D \(\frac{16}{7}\)
Answer & Solution
Correct Answer
(A) \(\frac{16 \sqrt{2}}{7}\)
Step-by-step Solution
Detailed explanation
Equation of line passing through the point \(P(1,2)\) which makes an angle \(45^{\circ}\) with the \(X\)-axis is \[ \begin{aligned} (y-2)=m(x-1) \text { and } m & =\tan \theta \\ & =\tan 45^{\circ}=1 \end{aligned} \] \(\therefore\) Equation is \(y-2=1(x-1)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- For a parallelogram \(A B C D\), if \(L\) and \(M\) are mid-points of \(B C\) and \(C D\), then \(\mathbf{A L}+\mathbf{A M}=\)AP EAMCET 2020 Medium
- The distance of a point \(\overrightarrow{\mathrm{a}}\) from the plane \(\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{m}}=\mathrm{q}\) is given by \(\frac{|\vec{a} \cdot \vec{m}-q|}{|m|}\). If the distance of the point \(\hat{i}+2 \hat{j}+3 \hat{k}\) from the plane \(\vec{r} \cdot(2 \hat{i}+6 \hat{j}-9 \hat{k})=-1\) is \(p\) and the distance of the origin from this plane is \(\mathrm{q}\), then \(\mathrm{p}-\mathrm{q}=\)AP EAMCET 2023 Medium
- If a diagonal of a square is along the line \(8 x-15 y=0\) and one of its vertices is \((1,2)\), then the equations of the sides of the square passing through this vertex areAP EAMCET 2020 Easy
- In a triangle \(A B C\), if \(a, b, c\) are in arithmetic progression and the angle \(A\) is twice the angle C, then \(\cos \mathrm{A}: \cos \mathrm{B}: \cos \mathrm{C}=\)AP EAMCET 2025 Medium
- The product of the four values of the complex number \((1+i)^{3 / 4}\) isAP EAMCET 2025 Hard
- The equation of bisectors of the angle between the lines represented by isAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- Two cards are drawn from a pack of 52 playing cards one after the other without replacement. If the first card drawn is a queen, then the probability of getting a face card from a black suit in the second draw isAP EAMCET 2025 Medium
- The points \(A(2,-1,4), B(1,0,-1), C(1,2,3)\) and \(D(2,1,8)\) form aAP EAMCET 2019 Easy
- \(\mathrm{K}_{\mathrm{c}}\) for the reaction
\(\mathrm{A}_2(\mathrm{~g}) \stackrel{\mathrm{T}(\mathrm{~K})}{\rightleftharpoons} \mathrm{B}_2(\mathrm{~g})\)
is 39.0. In a closed one litre flask, one mole of \(\mathrm{A}_2(\mathrm{~g})\) was heated to \(\mathrm{T}(\mathrm{K})\). What are the concentrations of \(\mathrm{A}_2(\mathrm{~g})\) and \(\mathrm{B}_2(\mathrm{~g})\) (in \(\mathrm{mol}^{-1}\) ) respectively at equilibrium?AP EAMCET 2024 Easy - A body is projected vertically from the surface of the earth of radius \(R\) with a velocity equal to half of the escape velocity. The maximum height reached by the body isAP EAMCET 2015 Medium
- Let \(f: R-\left\{\frac{-1}{2}\right\} \rightarrow R\) be defined by \(f(x)=\frac{x-2}{2 x+1}\). If \(\alpha\) and \(\beta\) satisfy the equation \(f(f(x))=-x\), then \(4\left(\alpha^2+\beta^2\right)=\)AP EAMCET 2022 Easy
- An electron is moving in Bohr's fourth orbit. Its de-Broglie wave length is \(\lambda\). What is the circumference of the fourth orbit?AP EAMCET 2005 Easy