WBJEE · Maths · Straight Lines
Let \(S\) be the set of points, whose abscissae and ordinates are natural numbers. Let \(P \in S\), such that the sum of the distance of \(P\) from (8,0) and (0,12) is minimum among all elements in \(S .\) Then, the number of such points \(P\) in \(S\) is
- A 1
- B 3
- C 5
- D 11
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
Sum of distances of point \(P\) from point (8,0) and (0,12) will be minimum, if points are collinear. Equation of line at point (8,0) and (0,12)…
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 what value of \(m, \frac{a^{\mathbf{m}+1}+b^{\mathbf{m}+1}}{a^{\mathbf{m}}+b^{\mathbf{m}}}\) is the arithmetic mean of ' \(a\) ' and ' \(b\) '?WBJEE 2009 Easy
- The smallest value of \(5 \cos \theta+12\) isWBJEE 2009 Easy
- If the circle \(x^{2}+y^{2}+2 g x+2 f y+c=0\) cuts the three circles \(x^{2}+y^{2}-5=0\) \(x^{2}+y^{2}-8 x-6 y+10=0\) and \(x^{2}+y^{2}-4 x+2 y-2=0\) at the extremities of their diameters, thenWBJEE 2014 Hard
- The solution of the differential equation \(y \frac{d y}{d x}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right]\) is (where, \(c\) is a constant)WBJEE 2014 Hard
- The points of extremum of \(\int_0^{x^2} \frac{t^2-5 t+4}{2+e^t} d t\) areWBJEE 2024 Medium
- The value of \(\lim _{n \rightarrow \infty} \frac{(n !)^{n}}{\frac{1}{n}}\) isWBJEE 2012 Hard
More PYQs from WBJEE
- Let \(n \geq 2\) be an integer. \(A=\left[\begin{array}{ccc}\cos (2 \pi / n) & \sin (2 \pi / n) & 0 \\ -\sin (2 \pi / n) & \cos (2 \pi / n) & 0 \\ 0 & 0 & 1\end{array}\right]\) and \(I\) is the identity matrix of order 3 . Then,WBJEE 2014 Hard
- Consider a tangent to the ellipse \(\frac{x^{2}}{2}+\frac{y^{2}}{1}=1\) at any point. The locus of the midpoint of the portion intercepted between the axes isWBJEE 2020 Medium
- If \(\mathbf{A}=\mathbf{B}+\mathbf{C}\) have scalar magnitudes of 5,4,3 units respectively, then the angle between \(A\) and \(\mathbf{C}\) isWBJEE 2012 Medium
- 1000 droplets of water having \(2 \mathrm{mm}\) diameter each coalesce to form a single drop. Given the surface tension of water is \(0.072 \mathrm{Nm}^{-1}\). The energy loss in the process isWBJEE 2016 Medium
- The solution of the differential equation \(\frac{d y}{d x}+\frac{y}{x \log _{e} x}=\frac{1}{x}\) under the condition \(y=1\) when \(x=e\) isWBJEE 2014 Medium
- A scientist proposes a new temperature scale in which the ice point is \(25 \mathrm{X}(\mathrm{X}\) is the new unit of temperature) and the steam point is \(305 \mathrm{X}\). The specific heat capacity of water in this new scale is \(\left(\operatorname{in} J \mathrm{kg}^{-1} \mathrm{X}^{-1}\right)\)WBJEE 2014 Medium