JEE 2023 — Mathematics PYQ

Step 1: Point $(1,-3)$ ko curve ki equation mein put karna

Chuniki point $(1,-3)$ curve par lie karta hai, isliye:

Step 2: Slope of Normal aur Tangent nikalna

Di gayi normal ki equation hai: $x-4y=13⟹4y=x-13⟹y=\frac{1}{4}x-\frac{13}{4}$.

• Slope of normal ($m_n$) = $\frac{1}{4}$

• Hum jante hain ki $m_t\cdot m_n=-1$, isliye Slope of tangent ($m_t$) = $-4$.

Step 3: Curve ko differentiate karke slope nikalna

Curve: $y(x+b)(x-2)=x-a$.

Point $(1,-3)$ par differentiate karte hain:

At $(1,-3)$:

Step 4: $a$ ki value find karna

$b=-3$ ko Equation 1 mein put karne par:

Step 5: Final calculation

Answer:

The value of $a+b$ is 4.