A straight line passing through the point (1, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the equation of the line be $y = m(x-1)$,which implies $\frac{mx-y}{m} = 1$.Given the curve equation $2x^2 + 5y^2 - 7x = 0$ ... $(i)$.Using th

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(D) Let the equation of the line be $y = m(x-1)$,which implies $\frac{mx-y}{m} = 1$.Given the curve equation $2x^2 + 5y^2 - 7x = 0$ ... $(i)$.Using the method of homogenization to find the pair of lines passing through the origin and points $A$ and $B$:$2x^2 + 5y^2 - 7x(1) = 0$Substituting $1 = \frac{mx-y}{m}$:$2x^2 + 5y^2 - 7x\left(\frac{mx-y}{m}\right) = 0$Multiplying by $m$:$2mx^2 + 5my^2 - 7mx^2 + 7xy = 0$$-5mx^2 + 7xy + 5my^2 = 0$.This is a homogeneous equation of the form $ax^2 + 2hxy + by^2 = 0$,where $a = -5m$,$2h = 7$,and $b = 5m$.For the lines to be perpendicular,the condition is $a + b = 0$.Here,$a + b = -5m + 5m = 0$.Since the sum of the coefficients of $x^2$ and $y^2$ is zero,the lines are perpendicular.Therefore,the angle subtended by the line segment $AB$ at the origin is $90^\circ$.

$A$ straight line passing through the point $(1,0)$ and not parallel to the $x$-axis intersects the curve $2x^2+5y^2-7x=0$ at two points $A$ and $B$. The angle subtended by the line segment $AB$ at the origin is (in $^\circ$)

Similar Questions

If $x+y-1=0$ and $2x-y+1=0$ are conjugate lines with respect to a circle $x^2+y^2-4x+2fy-1=0$,then $f=$

If the portion of the line $lx + my = 1$ falling inside the circle ${x^2} + {y^2} = {a^2}$ subtends an angle of $45^\circ$ at the origin,then

If the length of the tangents drawn from the point $(1, 2)$ to the circles $x^2 + y^2 + x + y - 4 = 0$ and $3x^2 + 3y^2 - x - y + k = 0$ are in the ratio $4 : 3$,then $k =$

The equation of the common tangent to the parabola $y^2=8x$ and the circle $x^2+y^2=2$ is $ax+by+2=0$. If $-\frac{a}{b} > 0$,then $3a^2+2b+1=$

The equation of a line inclined at an angle $\frac{\pi}{4}$ to the $X$-axis,such that the two circles $x^2 + y^2 = 4$ and $x^2 + y^2 - 10x - 14y + 65 = 0$ intercept equal lengths on it,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module