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Show that the plane {2}{x}-{2}{y}+{z}+{12}={0} touches the sph

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Show that the plane $2 x - 2 y + z + 12 = 0$ touches the sphere $x^{2} + y^{2} + z^{2} - 2 x - 4 y + 2 z - 3 = 0 .$

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Show that the plane

2 x - 2 y + z + 12 = 0

touches the sphere

x^{2} + y^{2} + z^{2} - 2 x - 4 y + 2 z - 3 = 0 .

10 mins ago

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Practice questions from similar books

Question 1

Let

P_{1} : 2 x + y - z = 3

and

P_{2} : x + 2 y + z = 2

be two planes. Then, which of the following statement(s) is (are) TRUE?The line of intersection of

P_{1}

and

P_{2}

has direction ratios

1, 2, - 1

(b) The line

\frac{3 x - 4}{9} = \frac{1 - 3 y}{9} = \frac{z}{3}

is perpendicular to the line of intersection of

P_{1}

and

P_{2}

P_{1}

and

P_{2}

60 o

(d) If

P_{3}

is the plane passing through the point

(4, 2, - 2)

and perpendicular to the line of intersection of

P_{1}

and

P_{2}

, then the distance of the point

(2, 1, 1)

from the plane

P_{3}

\frac{2}{3}

View solution

Question 2

A line AB in three-dimensional space makes angles

45^{o}

and

120^{o}

with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle q with the positive z-axis, then q equals

View solution

Question 3

The equation of the plane passing through the point

(1, 1, 1)

and perpendicular to the planes

2 x + y - 2 z = 5

and

3 x - 6 y - 2 z = 7

, is (A)

14 x + 2 y + 15 z = 3

(B)

14 x + 2 y - 15 z = 1

(C)

14 x + 2 y + 15 z = 31

(D)

14 x - 2 y + 15 z = 27

View solution

Question 4

Find the equation of the plane which is perpendicular to the plane

5 x + 3 y + 6 z + 8 = 0

and which contains the line of intersection of the planes

x + 2 y + 3 z - 4 = 0 a n d 2 x + y - z + 5 = 0

View solution

Question Text

Show that the plane

2 x - 2 y + z + 12 = 0

touches the sphere

x^{2} + y^{2} + z^{2} - 2 x - 4 y + 2 z - 3 = 0 .

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Show that the plane 2x−2y+z+12=0 touches the sphere x2+y2+z2−2x−4y+2z−3=0.

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Practice questions from similar books

Show that the plane $2 x - 2 y + z + 12 = 0$ touches the sphere $x^{2} + y^{2} + z^{2} - 2 x - 4 y + 2 z - 3 = 0 .$