A square is inscribed in the circle x^(2...

A square is inscribed in the circle `x^(2)+y^(2)-6x+8y-103=0` with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is

`sqrt(41)`

`sqrt(137)`

Text Solution

Verified by Experts

The correct Answer is:

Centre of given circle (3,-4) and Radius =`8sqrt2`
Vertices of inscribed square will be `(3 pm 8 , -4 pm 8) " " { because OP=PC=(8sqrt2)/sqrt2=8}`

So, vertex nearest to origin will be (-5,4)
Hence required distance =`sqrt41`

Topper's Solved these Questions

JEE MAIN REVISION TEST-3 (2020)
VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos
JEE Main Revision Test-9 | JEE-2020
VMC MODULES ENGLISH|Exercise SECTION 2|5 Videos

Similar Questions

Explore conceptually related problems

A square is inscribed in the circle x^(2)+y^(2)-2x+4y-93=0 with its sides are parallel to coordinate axes then vertices of square are

A square is incribed in a circle x^2+y^2-6x+8y-103=0 such that its sides are parallel to co-ordinate axis then the distance of the nearest vertex to origin, is equal to (A) 13 (B) sqrt127 (C) sqrt41 (D) 1

If an equilateral triangle is inscribed in the circle x^(2)+y^(2)-6x-4y+5=0 then its side is

A square is inscribed in the circle x^2+y^2-2x+4y+3=0 . Its sides are parallel to the coordinate axes. One vertex of the square is (1+sqrt(2),-2) (b) (1-sqrt(2),-2) (1,-2+sqrt(2)) (d) none of these

a square is inscribed in the circle x^2 + y^2- 10x - 6y + 30 = 0. One side of the square is parallel to y = x + 3, then one vertex of the square is :

A square is inscribed in the circle x^2+y^2-2x+4y-93=0 with its sides parallel to the coordinate axes. The coordinates of its vertices are (-6,-9),(-6,5),(8,-9),(8,5) (-6,-9),(-6,-5),(8,-9),(8,5) (-6,-9),(-6,5),(8,9),(8,5) (-6,-9),(-6,5),(8,-9),(8,-5)

The nearest point on the circle x^(2)+y^(2)-6x+4y-12=0 from (-5,4) is

A right angled isoceles triangle is inscribed in the circle x^(2)+y^(2)-6x+10y-38=0 then its area is (square units)

VMC MODULES ENGLISH-JEE Main Revision Test-6 | JEE-2020-MATHEMATICS

The value of r for which .^(20)C(r)xx.^(20)C(0)+.^(20)C(r-1)xx.^(20)C(...
Text Solution
|
The straight line x+2y=1 meets the coordinate axes at A and B. A circl...
Text Solution
|
The value of int(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx where [.] d...
Text Solution
|
Let A = ((0,2q,r),(p,q,-r),(p,-q,r)). If A A^(T) = I(3), then |p| is
Text Solution
|
A square is inscribed in the circle x^(2)+y^(2)-6x+8y-103=0 with its s...
Text Solution
|
The sum of the real values of x for which the middle term in the binom...
Text Solution
|
Two circles with equal are intersecting at the points (0, 1) and (0,-1...
Text Solution
|
Find the area bounded by the curve x^2=4y and the straight line x=4y-2...
Text Solution
|
The outcome of each of 30 items was observed, 10 items gave an outcome...
Text Solution
|
The sum of an infinite geometric series with positive terms is 3 and t...
Text Solution
|
If one real root of the quadratic equation 81x^2 + kx + 256=0 is cu...
Text Solution
|
If x satisfies the condition f(x)={x:x^2+3 0le11x} then maximum value ...
Text Solution
|
If q is false and (p^^q)harr r is also true then which of the followin...
Text Solution
|
Let a1, a2, a3, ?a10 are in G.P. if a3/a1 =25 then a9/a5 is equal to ...
Text Solution
|
Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...
Text Solution
|
Two integers are selected at random from the set {1, 2, …, 11}. Given ...
Text Solution
|
In a triangle, the sum of two sides is x and the product of the same t...
Text Solution
|
If xloge(logex)-x^2+y^2=4(ygt0)",then" dy//dx" at " x=e is equal to
Text Solution
|
If int(sqrt(1-x^2))/x^4dx=A(x) (sqrt(1-x^2))^m+C,for a suitable chose...
Text Solution
|
Let veca=hati+2hatj+4hatk, vecb=hati+lambdahatj+4hatk and vecc=2hati+4...
Text Solution
|