The value of -c- for which the set x- y- x2-y2-2 x - 1-x- y- x-y-c - 0 contains only one point is equal to

X^2+ y^2+2x 1=0 circle with C = ( 1, 0), R = √(2) x y + c = 0 is a tangent ⇒|c 1/√(2)|= √(2)⇒ c=3 or 1 If C = 3, the set will have infinite points ∴ C= 1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Length of Intercept Made by a Circle on a Straight Line

The value of ...

Question

The value of |c| for which the set ${(x, y) : x^{2} + y^{2} + 2 x \leq 1} \cup {(x, y) : x - y + c \geq 0}$ contains only one point is equal to ___

Open in App

Solution

$x^{2} + y^{2} + 2 x - 1 = 0$ circle with $C = (- 1, 0), R = \sqrt{2}$
x - y + c = 0 is a tangent
$\Rightarrow ∣ ∣ ∣ \frac{c - 1}{\sqrt{2}} ∣ ∣ ∣ = \sqrt{2} \Rightarrow c = 3 o r - 1$
If C = 3, the set will have infinite points
$∴ C = - 1 \Rightarrow | c | = 1$

Suggest Corrections

Similar questions

Q. Find the number of values of

c

for which the set

{(x, y) | x^{2} + y^{2} + 2 x \leq 1} \cap {(x, y) | x - y + c \geq 0}

contains only one point is common

Q. The value of 'c' for which the set

[(x, y) x^{2} + y^{2} + 2 x \leq 1] \cap [(x, y) | x - y + c \geq 0]

contains only one point in common is :

Q. The value of c for which the set

{(x, y) | x^{2} + y^{2} + 2 x \leq 1} \cap {(x, y) | x - y + c \geq 0}

contains only one point in common is?

Q. The value of c for which the set {(x, y) |

x^{2} + y^{2} + 2 x \leq 1

}

\cap

{

(x, y) | x - y + c

\geq 0

} contains only one point in common is

Q. The value of '

c

' for which the set

{(x, y) | x^{2} + y^{2} + 2 x \leq 1} \cap {(x, y) | x - y + c \geq 0}

contains only one point in common is

Join BYJU'S Learning Program

The value of |c| for which the set {(x,y):x2+y2+2x≤1}∪{(x,y):x−y+c≥0} contains only one point is equal to ___

x2+y2+2x−1=0 circle with C=(−1,0),R=√2 x - y + c = 0 is a tangent ⇒∣∣∣c−1√2∣∣∣=√2⇒c=3 or −1 If C = 3, the set will have infinite points ∴C=−1 ⇒|c|=1

The value of |c| for which the set ${(x, y) : x^{2} + y^{2} + 2 x \leq 1} \cup {(x, y) : x - y + c \geq 0}$ contains only one point is equal to ___

$x^{2} + y^{2} + 2 x - 1 = 0$ circle with $C = (- 1, 0), R = \sqrt{2}$
x - y + c = 0 is a tangent
$\Rightarrow ∣ ∣ ∣ \frac{c - 1}{\sqrt{2}} ∣ ∣ ∣ = \sqrt{2} \Rightarrow c = 3 o r - 1$
If C = 3, the set will have infinite points
$∴ C = - 1 \Rightarrow | c | = 1$