# math

posted by .

Show that x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal.

• math -

x^2 + y^2 -6x + 4y +2 = 0
can be rewritten as the equation of a circle, as follows.
(x-3)^2 + (y+2)^2 -9 -4 +2 = 0
(x-3)^2 + (y+2)^2 = 11
The center of the circle is (3,-2) and the radius is sqrt(11).
The other equation can be rewritten
(x+4)^2 + (y+1)^2 = 22 -17 = 5
Its center is at (-4,-1) and the radius is sqrt5

It looks to me like the two curves never intersect; I don't see how they can meet the definition of orthogonal.

## Similar Questions

1. ### calculus

if the tangent of two intersecting circles, at their points of intersection are perpendicular, the circles are said to be orthogonal. Show that the circles x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal. find the equation …
2. ### Math - Vectors

Prove that vector i,j and k are mutually orthogonal using the dot product. What is actually meant by mutually orthogonal?
3. ### Linear Algebra, orthogonal

The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is orthogonal, express v in terms of B where, v = 1 -2 -13 B = 1 1 2 , 1 3 -1 v is a matrix and B is a set of 2 …
4. ### Math

Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. …
5. ### calculus

two curves are orthogonal at a point of intersection of their tangents at that point cross at right angles. Show that the curves 2x^2+3y^2=5 and y^2=x^3 are orthogonal at (1,1) and (1,-1). Use parametric mode to draw the curves and …
6. ### Math

Show that A = [3 2 4 2 0 2 4 2 3] is distinguishable even though one eigenvector has algebraic multiplicity 2. Do this by brute force computation. Why would you expect this to be true, even without calculation?
7. ### Math

I'm doing a bunch of practice finals and I don't know how to approach this problem. Find a vector a such that a is orthogonal to < 1, 5, 2 > and has length equal to 6. If I want to find a vector that is orthogonal to <1,5,2>, …
8. ### st joseph

show that the circle x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal
9. ### linear algebra

Hello, how can I proof the next theorem? I have a linear transformation T(X) that can be express as T(X)=AX and A is an orthogonal matrix, then ||T (X)||=||X|| , I was doing this: ||T (X)||=sqrt(<AX,AX>) But I don't know what
10. ### Linear Algebra

Hi, I really need help with these True/False questions: (a) If three vectors in R^3 are orthonormal then they form a basis in R^3. (b) If Q is square orthogonal matrix such that Q^2018 = I then Q^2017 = Q^T. (c) If B is square orthogonal …

More Similar Questions