Let $$(-1$$, $$-1)$$ be the focus of a parabola and $$3x-y=8$$ be the tangent drawn to it at point (7$$,$$13) on the parabola. If ax $$+$$ by $$+$$ $$19=0$$ is the equation of directrix of the parabola then the value of $$a+b$$ is (where$$ a, b ∈ $$N)

Question

Let $$(-1$$, $$-1)$$ be the focus of a parabola and $$3x-y=8$$ be the tangent drawn to it at point (7$$,$$13) on the parabola. If ax $$+$$ by $$+$$ $$19=0$$ is the equation of directrix of the parabola then the value of $$a+b$$ is (where$$ a, b ∈ $$N)

Infinity Learn · Accepted Answer

Let foot of perpendicular from S(-1, -1) on 3x-y=8 is (α,β)∴α+13=β+1-1=1 ∴(α,β)=(-2,-2)Image of S about the tangent 3x-y=8S’(5, -3) which is on directrixLet point of intersection of tangent and directrix =Qh,3h-8P(7,13) is poiint of contact of tangent∠QSP=90°⇒slope of QSSlope of SP=-1 ⇒3h-7h+174=-1⇒h=95⇒Q=95,-135 Slope of directrix=-13/5+39/5-5=-18 ⇒Equation of directrix y+3=-18x-5⇒x+8y+19=0 ∴Eqn of directrix is 8y+x+19=0 ⇒a+b=9

Let (-1, -1) be the focus of a parabola and 3x-y=8 be the tangent drawn to it at point (7,13) on the parabola. If ax + by + 19=0 is the equation of directrix of the parabola then the value of a+b is (where a, b $\in$ N)

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Let (-1, -1) be the focus of a parabola and 3x-y=8 be the tangent drawn to it at point (7,13) on the parabola. If ax + by + 19=0 is the equation of directrix of the parabola then the value of a+b is (where a, b ∈ N)

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Let (-1, -1) be the focus of a parabola and 3x-y=8 be the tangent drawn to it at point (7,13) on the parabola. If ax + by + 19=0 is the equation of directrix of the parabola then the value of a+b is (where a, b $\in$ N)