Question

Prove that every point on the line y = 6 − x is outside the circle with equation (x + 3)^2 + (y − 1)^2 = 16 (recall that a point (a, b) is outside the circle means that (a + 3)^2 + (b − 1)^2 ≥ 16).

Proof from scratch please!

Answer #1

Prove that there exists a point (a, b) inside the circle (x −
3)^2 + (y − 2)^2 = 13 such that a < 0 and b > 3.5. (recall:
the point (a, b) is inside the circle means that (a − 3)^2 + (b −
2)^2 ≤ 13)

Find an equation for the line tangent to the circle x^(2)+y^(2)=
25 at the point(3,−4).

Recall the equation for a circle with center (h,k)(h,k) and
radius rr. At what point in the first quadrant does the line with
equation y=2x+1y=2x+1 intersect the circle with radius 3 and center
(0, 1)?
x=?
y=?

At what point in the first quadrant does the line with
equation y = x 2+ intersect the circle with radius 6 and center
(-1,0)?

a circle has the equation: (x+5)2 + (y-3)2
= 37. What is the equation of the line tangent to the circle at the
point whose coordinates are (1,4)? please write in ax+ by = C form
.

Given: equation of circle k (x - 3)2 + (y -
2)2 = 36 and equation of the line g: y = mx + 8.
What are the conditions of m under which: a) m does not touch
the circle b) m intersects the circle in one point c) m intersects
the circle in two points?

A
tangent to a circle at the point (5,5) passes through the origin.
The line with equation 3y=x+2 is a normal to the circle.
(i) Show all working, find the equation of the circle.
(ii) Find the coordinates of the point on the circle whih is
nearest to the x-axis.

Find the area between line y = 3-x and circle x ^ 2 +
y ^ 2 = 9 using integral.

1.
Find the point on the line y = x − 6 that is closest to the origin
2. Find the rate of change ds/dt of the function S= x^2+y^2
when x=9, y=15, dx/dt=2, dy/dt=-1

1) Prove that for all real numbers x and y, if x < y, then x
< (x+y)/2 < y
2) Let a, b ∈ R. Prove that:
a) (Triangle inequality) |a + b| ≤ |a| + |b| (HINT: Use Exercise
2.1.12b and
Proposition 2.1.12, or a proof by cases.)

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