In the figure, O is the centre of the circle with radius r and P(a,b) is a point on the circle. AB is the diameter of the circle.  a) Prove that a2+b2=r2 b) Prove by the analytic approach that AP is perpendicular to PB.

Q: Show complete solutions with clear figures. Determine the tangent length from (-4,-4) to the circle…

A: diameter length=Distance between two points (2, 3) and (4, -3)d=(4-2)2+(-3-3)2d=40r=402center (h,…

Q: In Cartesian space, line segment P¡P2 has endpoints P(-2, 3, 5) and P2(2, – 1, -7). a) Find midpoint…

A: Since, we have been given up the endpoints P1(a1,b1,c1)=(-2,3,5)and P2(a2,b2,c2)=(2,-1,-7)Therefore,…

Q: The locus of z when a) A parabola b) An arc of a circle Oc) A straight line d) A circle |z-2+i…

A:

Q: Show that the equation of a circle passing through the origin and having intercepts a and b on real…

A:

Q: Find the distance from the point (0,3,0) to the plane 7x + 4y + 4z = 7. The distance from the point…

A: The Distance between a point to the plane  is given as follows

Q: How much must "t" be so that points P(2,1); Q(-2,1) and R(0,t) are vertices of an isosceles triangle…

A:

Q: 4) Determine if (,1) is a point on the unit circle V3 5) If the point (x,) lies on the unit circle,…

A: Standard form of a circle is given by the equation (x-h)2+(y-k)2=r2, where (h,k) is the center of…

Q: (r, 0) 4, – 3+ 27 (r > 0) %3D

A:

Q: Evaluate the line itegral where C is the upper half of the circle z +y = 3.

A:

Q: Use the applet to translate quadrilateral ABCD 2 units left to create quadrilateral A'B'C'D', then…

A:

Q: 14) What is the y-coordinate of the midpoint of WU? Z 2+ -4-2 X2 •Y -2+ V U a) -2.5 b) -1.5 c) -0.5…

A: Explanation:

Q: The radical center does not existif the circles are concentric TRUE FALSE

A:

Q: For the points P and Q, find the distance d(P, Q). 18) P(-7, -1), Q(5, -3) A) 14 B) 140 C) 140 /35…

A:

Q: Consider two circles in a plane. The first circle, C₁, has a radius of r₁ and is centered at point…

A: For the centers of the two circles C1 and C2 to coincide, the coordinates of their centers must be…

Q: Consider the points (1,2) and (5,4). a) Plot the points and use the Pythagorean Theorem to find the…

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: A Find the Distance from the point (2,-6) to the line 3x+ 4y t6=0 B Find the distance between the…

A:

Q: Maciek swims in a 25 m long pool. At one end of the pool the depth is 3 m, and at the other 1.5 m.…

A: Given: Length of  pool BE=25m To find: Capacity of pool

Q: Determine the expressions equivalent to 3x²y², 3x8y3 a) 9x24y9 3x°y5 3xly6 x24y9 1 x18y3

A:

Q: 3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The corners…

A: a)Co-ordinates of GG0+7.52,0+02,0+02=G154,0,0Co-ordinates of P∵P lies on the  xy planeso…

Q: ) Prove that r1 and r2 intersect and calculate their intersection B) What is the angle between r1…

A:

Q: 15. Complete the squares on x- and y-terms of the circle: 4x + 24x + 4y + 36y =0. SLO 12

A:

Q: ㅠ Use Green's theorem to find: where C is the circle x² + y² = 4 going counter-clockwise. -8T […

A:

Q: Use Green's Theorem to evaluate §+(x² - y²)ẩx + xảy, where C is the circle x² + y² = 9. Select one:…

A:

Q: Evaluate Re z? dz, C: the unit circle (counterclockwise).

A:

Q: Find the distances: a. Between 4 = (3+t,-2+ 3t,-t) and l2 = (1+ 2t, t,5+ 4t). %3D %3D b. Between the…

A: 3-d geometry is the concept that deals with 3 dimensional figures. In order to find distance between…