# Tagged Questions

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### Equation of a line with a positive gradient [on hold]

Two straight lines passing through the point (0,2) are tangent to the graph of the function y=1-x^2. Find the equation of the line with a positive gradient.
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### Need a solution to find the locus of an equation. [on hold]

Find the equation of the locus of a point which moves so that its distance from $(a,0)$ is equal to its distance from the $y$-axis. The answer is $$y^2 - 2ax + a^2 =0$$ Please can someone find the ...
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### getting the slopes of the sides of an equilateral triangle given 2 points

I want to get the slopes of an equilateral triangle given the 2 vertices. Let's say they are (0, 0) and (5, 5). Graphing this would give 2 triangles forming a diamond. I tried to use distance formula ...
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### Omitting $i$ in calculations

Is it possible in various calculations related to the complex plane which also include analytic geometry , calculating distances etc, to omit $i$ and treat the imaginary axis as simply the cartesian ...
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### Doubt on locus of a median point

I'm learning about geometric locus and ain't had an good time, I'm struggling with this problem: By the way, any study resource on geometric locus is welcome! Given an segment $AB$ formed by points ...
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### Graphs interpretation question

Suppose we have a prarbola $y^2 = 2px$ ....this is in fact $y = \sqrt{2px}$, so we plot it like a square root function, so it has no applied values for less than zero. However I saw in my textbook ...
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### Find an unknown coefficient in a line equation…

So, I have to find the unknown coefficient in this line: $$x+y+C=0$$ so that it is a tangent to this circle: $$x^2+y^2-5x-7y+6=0$$ I've transformed the circle equation to this form: ...
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### How do i find the radius and the center of these circles

Please help me with my math Radius Homework Help is really appreciated! PS: Pls Don't be bothered by my erasure on my sheet, those 4 question are unanswered. Instructors' formula is x^2 + y^2 = r^2 ...
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### Find plane which parallel to two vectors $L_{1} ( 3,1,10)$ and $L_{2}(1,-1,1)$ passes through a point $M(7,-10,3)$

I`m trying to find a plane which parallel to two vectors $L_{1} ( 3,1,10)$ and $L_{2}(1,-1,1)$ passes through a point $M(7,-10,3)$ what I tried to do is to create $L_{1}L_{2}$ vector then to create ...
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### Find the projection of the point on the plane

I want to find the projection of the point $M(10,-12,12)$ on the plane $2x-3y+4z-17=0$. The normal of the plane is $N(2,-3,4)$. Do I need to use Gramâ€“Schmidt process? If yes, is this the right ...
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### Find the point of intersection of the straight line $\frac{X+1}{4}=\frac{Y-2}{-2}=\frac{Z+6}{7}$ and plane $3X+8Y-9Z=0$

Find the point of intersection of the straight line $$\frac{X+1}{4}=\frac{Y-2}{-2}=\frac{Z+6}{7}$$ and plane $3X+8Y-9Z=0$ the point of the line is $M(-1,2,-6)$ and direction vector of the line is ...
### Explain what are the projections of the point $P(a,b,c)$ on the planes of the coordinate system.
I want to explain what are the projections of the point $P(a,b,c)$ on the planes of the coordinate system. the meaning is that if it on $XY$ plane so it will be $P(a,b,0)$ and so on? Thanks!
### Check whether the three vectors $A(2,-1,2),B(1,2,-3),C(3,-4,7)$ are in the same plane
I want to check if three vectors are in the same plane, the vectors being $$A(2,-1,2),B(1,2,-3),C(3,-4,7).$$ What I did so far is to create vector $AB ( -1,3,-5)$ and build the plane equation ...