If the straight line x−$$2y+1=0$$ intersects the circle $$x2+y2=25$$ in points P and Q, then the coordinates of the point of intersection of tangents drawn at P and Q to the circle $$x2+y2=25$$ are

Question

If the straight line x−$$2y+1=0$$ intersects the circle $$x2+y2=25$$ in points P and Q, then the coordinates of the point of intersection of tangents drawn at P and Q to the circle $$x2+y2=25$$ are

Infinity Learn · Accepted Answer

Let $$R(h$$,$$k)$$ be the point of intersection of tangents drawn at P and Q to the given circle. Then, PQ is the chord of contact of tangents drawn from R to $$x2+y2=25$$ So its equation is $$hx+ky$$−$$25=0$$.                  …(i)It$$ is given that the equation of PQ isx−$$2y+1=0$$                          …$$(ii)Since$$ $$(i) and (ii) represent the same line. ∴ $$h1=k$$−$$2=$$−$$251$$⇒$$h=$$−$$25$$,$$k=50Hence$$, the required point is $$(-$$ $$25$$, $$50)$$.

If the straight line $x - 2 y + 1 = 0$ intersects the circle $x^{2} + y^{2} = 25$ in points $P$ and $Q$ , then the coordinates of the point of intersection of tangents drawn at $P$ and $Q$ to the circle $x^{2} + y^{2} = 25$ are

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If the straight line x−2y+1=0 intersects the circle x2+y2=25 in points P and Q, then the coordinates of the point of intersection of tangents drawn at P and Q to the circle x2+y2=25 are

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If the straight line $x - 2 y + 1 = 0$ intersects the circle $x^{2} + y^{2} = 25$ in points $P$ and $Q$ , then the coordinates of the point of intersection of tangents drawn at $P$ and $Q$ to the circle $x^{2} + y^{2} = 25$ are