AP EAMCET · Maths · Three Dimensional Geometry
The point in the xy-plane which is equidistant from the points \(\mathrm{A}(2,0,3), \mathrm{B}(0,3,2)\) and \(\mathrm{C}(0,0,1)\) has the coordinates
- A \((3,2,0)\)
- B \((2,3,0)\)
- C \((2,0,8)\)
- D \((0,3,1)\)
Answer & Solution
Correct Answer
(A) \((3,2,0)\)
Step-by-step Solution
Detailed explanation
Let the point in the xy-plane be \(P(x,y,0)\). \(PA^2 = PC^2 \Rightarrow (x-2)^2 + y^2 + (0-3)^2 = x^2 + y^2 + (0-1)^2\) \((x-2)^2 + 9 = x^2 + 1\) \(x^2 - 4x + 4 + 9 = x^2 + 1\) \(-4x + 13 = 1 \Rightarrow -4x = -12 \Rightarrow x = 3\)…
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
- If \(\operatorname{det}(\mathrm{AB})=(\operatorname{det} \mathrm{A})(\operatorname{det} \mathrm{B})\) and \(\mathrm{A}\) is a non-singular matrix of \(\operatorname{order} 3 \times 3\), then \(\operatorname{det}(\operatorname{adj} A)=\)AP EAMCET 2023 Easy
- If \(A=\left[\begin{array}{ccc}1 & -3 & 2 \\ -2 & 1 & 3 \\ 3 & 2 & -1\end{array}\right]\) then \(A^2 \operatorname{Adj} A=\)AP EAMCET 2022 Easy
- \(\int \frac{x+1}{x^3-1} d x=\)AP EAMCET 2025 Medium
- Lagrange's mean value theorem is not applicable in \([0,1]\) to the functionAP EAMCET 2017 Medium
- If two of the lines represented by \(2 x^3+x^2 y+y^3=0\) are mutually perpendicular, then the slope of the third line isAP EAMCET 2017 Easy
- The locus of the point of intersection of the normals to the parabola \(x^2=8 y\), which are at right angles to each other, isAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- A ball is dropped from a tower of height \(80 \mathrm{~m}\). The time it takes to cover the last \(50 \%\) of its fall is
(acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )AP EAMCET 2022 Easy - If \(\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\), \(\mathbf{c}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\), \(\mathbf{n}\) is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) and \(\theta\) is the angle between \(\mathbf{c}\) and \(\mathbf{n}\) then \(\sin \theta=\)AP EAMCET 2018 Medium
- A metallic solid undergoes Frenkel defect. Its original mass, volume and density are \(M_0, V_0\) and \(D_0\) respectively. After Frenkel defect the mass, volume and density are \(M, V\) and \(D\) respectively. The variations of \(M, V\) and \(D\) after Frenkel defect areAP EAMCET 2020 Medium
- \(\int \frac{3 x^9+7 x^8}{\left(x^2+2 x+5 x^8\right)^2} d x=\)AP EAMCET 2024 Medium
- Let \(S\) be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6 ) and let \(E_k=\{(a, b) \in S: a b=k\}\) for \(k \geq 1\).
If \(p_k+P\left(E_k\right)\) for \(k \geq 1\), then the correct among the following, isAP EAMCET 2008 Medium - If the average translational kinetic energy of a molecule in a gas is equal to the kinetic energy of an electron accelerating from rest through \(10 \mathrm{~V}\), then the temperature of the gas molecule is
\[
\left(\text { Boltzmann constant }=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)
\]AP EAMCET 2017 Easy