WebbWe know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius. So add 21 to both sides to get the constant term to the righthand side of the equation. x^2 + y^2 -4y = 21. Then complete the square for the y terms. x^2 + y^2 - 4y + 4 = 21 + 4. Webb13 juni 2016 · Using the tangent equations here we have: Parabola: y2 = 4x Tangent at P(p2, 2p): y ⋅ 2p = 2(x + p2) ⇒ x − py + p2 = 0 For this line to be a tangent to the circle x2 + y2 = 1 2, its distance from (0, 0) must equal the radius of the circle 1 √2. p2 √12 + p2 = 1 √2 2p4 − p2 − 1 = 0 (2p2 + 1)(p2 − 1) = 0 ∵ p2 > 0 ∴ p2 = 1 p = ± 1

Example 7 - Find area lying above x-axis, included b/w circle

Webb26 sep. 2024 · IIT JEE CONIC SECTIONS The parabola `y^2=4x` and the circle having its center at (6, 5) intersec... 1,752 views Sep 26, 2024 12 Dislike Doubtnut 2.18M subscribers This is the Solution of... Webb5 feb. 2024 · The point of intersections with the parabola y2 = 4x were found out to be (4, 4) and (9, 6) Let R be (9, 6). Hence circle C2 passes through (9,6) and focus (1,0) This … city cars henderson

The point on the parabola ${{y}^{2}}=4x$ which are closest to

WebbCorrect options are A) and C) Given parabola and circle are y2=9xand x2+y2−4x−6=0respectively. Now solving these, x2+9x−4x−6=0⇒x2+5x−6=0⇒(x−1)(x+6)=0⇒x=1,−6but x<0is not a solution Thus x=1,and corresponding y=3,−3 Hence point of intersection of the parabola and circle are … WebbA line is a common tangent to the circle (x–3)2+y2 =9 and the parabola y2 = 4x. If the two points of contact (a,b) and (c,d) are distinct and lie in the first quadrant, then 2(a+c) is equal to Solution Circle : (x−3)2+y2 = 9 Parabola : y2 =4x Let common tangent equation be y =mx+ a m ⇒ y= mx+ 1 m ⇒ m2x−my+1=0 WebbAn equation of a tangent common to the parabolas y2 = 4x and x 2 = 4y is (A) x – y + 1 = 0 (B) x + y – 1 = 0 (C) x + y + 1 = 0 (D) y = 0 9. The line 4x − 7y + 10 = 0 intersects the parabola, y2 = 4x at the points A & B. The co-ordinates of the point of intersection of the tangents drawn at the points A & B are: 7 5 5 7 5 7 7 5 city cars games