What is the equation of the chord of the circle x^2+y^2=16, passing through (2,3).
Pls help!
If lines 7x-2y+10=0 and 7x+2y-10=0 forms an isoceles triangle with the line y=2. Then what is the area of the triangle.
Pls help
There are infinitely many chords passing through any point within the circle. Two such chords, easy to describe are
x=2 and y=3.
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Clearly, the vertex of the triangle is at (0,5), so the altitude is 3.
The base of the triangle goes between (-6/7,2) and (6/7,2), so it has a length of 12/7.
Now you can get the area...
To find the equation of the chord passing through the point (2,3) in the circle x^2 + y^2 = 16, we need to use the properties of a circle.
Step 1: Find the center and radius of the circle
The equation of the circle is already given as x^2 + y^2 = 16. Comparing this equation with the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, we can see that the center is at the origin (h, k) = (0, 0) and the radius (r) is √16 = 4.
Step 2: Find the equation of the line passing through (2,3) and the center (0,0)
The slope (m) of the line passing through two points, (x1, y1) and (x2, y2), can be determined using the formula: m = (y2 - y1)/(x2 - x1).
Using the coordinates (2,3) and (0,0), we get:
m = (0 - 3) / (0 - 2)
= -3 / -2
= 3/2
So, the slope of the line is 3/2.
Step 3: Use point-slope form to find the equation of the line
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is its slope.
Substituting the values:
y - 3 = (3/2)(x - 2)
Expanding and simplifying:
y - 3 = (3/2)x - 3
y = (3/2)x
Now you have the equation of the chord passing through (2,3) in the circle x^2 + y^2 = 16 as y = (3/2)x.