Find the plane that passes through the origin and intersects with the conical surface as a circle

Find the plane that passes through the origin and intersects with the conical surface as a circle

First, write out the equation of the cone axis, and then write out the expression of the plane perpendicular to the axis. Bring the origin coordinate into the expression to get the variable coefficient in the expression. The expression obtained is the plane that passes through the origin and intersects with the cone surface as a circle

Planar sections
Make a plane through the intersection of two planes 4x-y + 3z-1 = 0 and X + 5y-z + 2 = 0, and make it parallel to the Y axis. The equation of the plane is ~ thank you ~ the more detailed the steps, the better. It's better to be simple and easy to understand
Straight line X-Y + Z + 5 = 0
The standard equation of 5x + 8y + 4Z + 36 = 0
Two questions~
X / 4 = (y-4) / 1 = (Z-1) / 3~

First, find any point on the intersection of two planes 4x-y + 3z-1 = 0 and X + 5y-z + 2 = 0, and then cross multiply the normal vectors (4, - 1,3) of two planes by (1,5, - 1) to get the direction vector of the intersection line. Then, set the normal vector (a, 0, c) of the plane to be solved by being parallel to the Y axis. The normal vector (a, 0, c) of the plane to be solved is perpendicular to the direction vector of the intersection line, so the point multiplication is zero, Now that we know the normal vector of a point and a plane, we can easily write the equation of a plane
The second question is not very clear about what you said the standard equation is. In fact, what you wrote should be the standard equation. Maybe I remember wrong. Let's talk about how to rewrite it into a point equation
The point direction equation of the straight line {X-Y + Z + 5 = 0,5x + 8y + 4Z + 36 = 0} is required. First, the direction vector of the straight line is required. Similarly, the direction vector of the intersection line is obtained by the cross product of the normal vectors of two planes (1, - 1,1) (5,8,4). It is easy to find a point on the intersection line. So far, given the direction vector of the intersection line and a point on the intersection line, the point direction equation can be easily written
That's the pointwise equation. You can work it out according to the above

It is proved that a real symmetric matrix is a positive definite matrix if and only if its eigenvalues are positive

1. There is a theorem in Higher Algebra: for any n-order real symmetric matrix A, there exists an n-order orthogonal matrix T, which makes t'at diagonal, and the elements on the diagonal are its eigenvalues. Thus, we prove that (1) sufficiency: when the eigenvalues of symmetric matrix A are all positive, the elements on the diagonal of diagonal matrix t'at

1. Decomposition factor A & # 178; - B & # 178; - 2A + 2B

a²-b²-2a+2b
=(a+b)(a-b)-2(a-b)
=(a-b)(a+b-2)

If the value of fraction x + 2 / (x + 2) (x + 3) is positive, then the value range of X is
If the value of fraction x + 2 / [(x + 2) (x + 3)] is positive, then the value range of X is_____

If the value of fraction x + 2 / [(x + 2) (x + 3)] is positive
Then x + 2 > 0 and (x + 2) (x + 3) > 0, or x + 20
If x + 2 > 0
x>-2
If (x + 2) (x + 3) > 0
Then x + 2 > 0 and X + 3 > 0, or x + 2-3, or x0 and (x + 2) (x + 3) > 0
If you want x + 2

Let f (x) = (2x + 1) / (4x + 3) (x belongs to R and X ≠ - 3 / 4), then the value of f ^ - 1 (2) is
Seeking process````
How to find out his inverse function by using function f (x) = (2x + 1) / (4x + 3)````
I know I don't need to ask, but I want to know how to ask
y=(2x+1)/(4x+3)
x=(1-3y)/(4y-2)
How does x = (1-3y) / (4Y-2) come out?

2=(2x+1)/(4x+3)
x=-5/6
f^-1(2)=-5/6
--------------
This problem does not need to solve the inverse function, if required, it is to solve an equation
y=(2x+1)/(4x+3)
x=(1-3y)/(4y-2) y≠1/2
f^-1(x)=(1-3x)/(4x-2) x≠1/2

If the image of inverse scale function y = K / X (k is not equal to 0) passes through point (a, - a), then K satisfies ()?

Because the inverse scale function image passes through (a, - a)
Substituting x = a, y = - a into the original formula
K = - a squared
So K is less than or equal to 0
I'm a sophomore in junior high school. I used it just after I finished my study

If the sum of two rational numbers is negative and the product is positive, then the two rational numbers ()
A. All positive numbers B. one positive and one negative C. all negative numbers D. not sure

∵ the product of two rational numbers is positive, ∵ the two numbers have the same sign; and ∵ their sum is negative, ∵ the two numbers have the same negative

0.5 (x-3) - 4x + 1 = 0

0.5 (x-3) - 4 / 5x + 1 = 0 Solution & nbsp; 0.5x-1.5-4 / 5x + 1 = 0 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; - 3 / 10x = 0.5 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = - 5 / 3 answer: x = - 5 / 3 hope to help you make progress in your study. If you have any questions, please ask, If you have any other questions, please help me. If you are satisfied with my answer, please click Select as satisfied answer. This is your greatest affirmation to me. Thank you!

The square of x plus the solution that 11x equals 12? I can't understand this equation?

x²+11x=12
x²+11x-12=0
(x+12)(x-1)=0
x=-12,x=1