Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2018 · Mathematics · Three Dimensional Geometry

What is the equation to the sphere whose centre is at (-2,3,4) and...

What is the equation to the sphere whose centre is at (−2,3,4)(-2,3,4) and radius is 6 units?

Options

  1. Ax2+y2+z2+4x−6y−8z=7x^2+y^2+z^2+4 x-6 y-8 z=7
  2. Bx2+y2+z2+6x−4y−8z=7x^2+y^2+z^2+6 x-4 y-8 z=7
  3. Cx2+y2+z2+4x−6y−8z=4x^2+y^2+z^2+4 x-6 y-8 z=4
  4. Dx2+y2+z2+4x+6y+8z=4x^2+y^2+z^2+4 x+6 y+8 z=4

Correct answer

A. x2+y2+z2+4x−6y−8z=7x^2+y^2+z^2+4 x-6 y-8 z=7

Step-by-step solution

Given, centre of sphere (h,k,l)=(−2,3,4)(h, k, l)=(-2,3,4) radius (r)=6(\mathrm{r})=6 units. Equation of sphere is (x−h)2+(y−k)2+(z−ℓ)2=r2(x-h)^2+(y-k)^2+(z-\ell)^2=r^2⇒(x+2)2+(y−3)2+(z−4)2=62⇒x2+4x+4+y2−6y+9+z2−8z+16=36⇒x2+y2+z2+4x−6y−8z=7\begin{aligned} & \Rightarrow(\mathrm{x}+2)^2+(\mathrm{y}-3)^2+(\mathrm{z}-4)^2=6^2 \\ & \Rightarrow \mathrm{x}^2+4 \mathrm{x}+4+\mathrm{y}^2-6 \mathrm{y}+9+\mathrm{z}^2-8 \mathrm{z}+16=36 \\ & \Rightarrow \mathrm{x}^2+\mathrm{y}^2+\mathrm{z}^2+4 \mathrm{x}-6 \mathrm{y}-8 \mathrm{z}=7 \end{aligned}$$
Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: If the… NDA 2026Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P… NDA 2026Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question… NDA 2026Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P… NDA 2026Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question… NDA 2026Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: What is… NDA 2026For the following two (02) items: A plane P is parallel to the line having direction… NDA 2025For the following two (02) items: Suppose S is the sphere with the smallest radius that… NDA 2025A(1, 2, -1) , B(2, 5, -2) and C(4, 4, -3) are three vertices of a rectangle. What is the… NDA 2025If a line (x+1)/(p) = (y-1)/(q) = (z-2)/(r) where p = 2q = 3r , makes an angle θ with the… NDA 2025What is the equation of the plane passing through the point (1, 1, 1) and perpendicular… NDA 2025For the following two (02) items: Let A(1, -1, 0) , B(-2, 1, 8) and C(-1, 2, 7) are three… NDA 2025For the following two (02) items: Suppose S is the sphere with the smallest radius that… NDA 2025If a line in 3 dimensions makes angles α , β and γ with the positive directions of the… NDA 2025A line makes angles α , β and γ with the positive directions of the coordinate axes. If a… NDA 2025For the following two (02) items: A plane P is parallel to the line having direction… NDA 2025 Full Three Dimensional Geometry list Three Dimensional Geometry JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs